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General Composite Non-Abelian Strings and Flag Manifold Sigma ModelsAug 22 2019We fully investigate the symmetry breaking patterns occurring upon creation of composite non-Abelian strings: vortex strings in non-Abelian theories where different sets of colours have different amounts of flux. After spontaneous symmetry breaking, there ... More
Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical ConceptsAug 22 2019We give an elementary introduction to the theory of causal fermion systems, with a focus on the underlying physical ideas and the conceptual and mathematical foundations.
A Gauge Fixing Procedure for Causal Fermion SystemsAug 22 2019Causal fermion systems incorporate local gauge symmetry in the sense that the Lagrangian and all inherent structures are invariant under local phase transformations of the physical wave functions. In the present paper it is explained and worked out in ... More
Superstring Amplitudes, Unitarity, and Hankel Determinants of Multiple Zeta ValuesAug 22 2019The interplay of unitarity and analyticity has long been known to impose strong constraints on scattering amplitudes in quantum field theory and string theory. This has been highlighted in recent times in a number of papers and lecture notes. Here we ... More
Spectral rigidity of random Schrödinger operators via Feynman-Kac formulasAug 22 2019We develop a technique for proving number rigidity (in the sense of Ghosh-Peres) of the spectrum of general random Schr\"odinger operators (RSOs). Our method makes use of Feynman-Kac formulas to estimate the variance of exponential linear statistics of ... More
Signatures of Many-Particle InterferenceAug 22 2019This Tutorial will introduce the mathematical framework for describing systems of identical particles, and explain the notion of indistinguishability. We will then focus our attention on dynamical systems of free particles and formally introduce the concept ... More
M. Kontsevich's graph complexes and universal structures on graded symplectic manifolds IAug 22 2019In the formulation of his celebrated Formality conjecture, M. Kontsevich introduced a universal version of the deformation theory for the Schouten algebra of polyvector fields on affine manifolds. This universal deformation complex takes the form of a ... More
Quantum Algorithms for Portfolio OptimizationAug 22 2019We develop the first quantum algorithm for the constrained portfolio optimization problem. The algorithm has running time $\widetilde{O} \left( n\sqrt{r} \frac{\zeta \kappa}{\delta^2} \log \left(1/\epsilon\right) \right)$, where $r$ is the number of positivity ... More
Exact results for the boundary energy of one-dimensional bosonsAug 22 2019We study bosons in a one-dimensional hard wall box potential. In the case of contact interaction, the system is exactly solvable by Bethe ansatz, as first shown by Gaudin in 1971. Although contained in the exact solution, the boundary energy for this ... More
Brown Measures of Free Circular and Multiplicative Brownian Motions with Probabilistic Initial PointAug 22 2019Given a selfadjoint random variable $x_0$ and a unitary random variable $u$, different from Haar unitary, free from the free circular Brownian motion $c_t$ and the free multiplicative Brownian motion $b_t$, we use the Hamilton-Jacobi method to compute ... More
Mass-deformed $\mathcal{N} = 3$ Supersymmetric Chern-Simons-Matter TheoryAug 21 2019The maximal extension of supersymmetric Chern-Simons theory coupled to fundamental matter has $\mathcal{N} = 3$ supersymmetry. In this short note, we provide the explicit form of the action for the mass-deformed $\mathcal{N} = 3$ supersymmetric $U(N)$ ... More
Towards an M5-Brane Model II: Metric String StructuresAug 21 2019We clarify the mathematical formulation of metric string structures, which play a crucial role in the formulation of six-dimensional superconformal field theories. We show that the connections on non-abelian gerbes usually introduced in the literature ... More
Random Quantum BatteriesAug 21 2019Quantum nano-devices are fundamental systems in quantum thermodynamics that have been the subject of profound interest in recent years. Among these, quantum batteries play a very important role. In this paper we lay down a theory of random quantum batteries ... More
Integrability and cycles of deformed ${\cal N}=2$ gauge theoryAug 21 2019To analyse pure ${\cal N}=2$ $SU(2)$ gauge theory in the Nekrasov-Shatashvili (NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary Differential Equation/Integrable Model (ODE/IM) correspondence, and in particular its (broken) discrete symmetry ... More
Virtual clusters model on branching random graphs for confined fluid thermodynamics in heterogeneous solid geometryAug 21 2019Fluid properties near rough surfaces are crucial in both a description of fundamental surface phenomena and modern industrial material design implementations. One of the most powerful approach to model real rough materials is based on the surface representation ... More
On an optimal potential of Schrödinger operator with prescribed $m$ eigenvalueAug 21 2019The purpose of this paper is twofold: firstly, we present a new type of relationship between inverse problems and nonlinear differential equations. Secondly, we introduce a new type of inverse spectral problem, posed as follows: for a priori given potential ... More
Derivation of coupled KPZ-Burgers equation from multi-species zero-range processesAug 21 2019We consider the fluctuation fields of multi-species weakly-asymmetric zero-range interacting particle systems in one dimension, where the mass density of each species is conserved. Although such fields have been studied in systems with a single species, ... More
Essential singularities of fractal zeta functionsAug 21 2019We study the essential singularities of geometric zeta functions $\zeta_{\mathcal L}$, associated with bounded fractal strings $\mathcal L$. For any three prescribed real numbers $D_{\infty}$, $D_1$ and $D$ in $[0,1]$, such that $D_{\infty}<D_1\le D$, ... More
Data-driven model reduction, Wiener projections, and the Mori-Zwanzig formalismAug 21 2019First-principles models of complex dynamic phenomena often have many degrees of freedom, only a small fraction of which may be scientifically relevant or observable. Reduced models distill such phenomena to their essence by modeling only relevant variables, ... More
The Complementary Information Principle of Quantum MechanicsAug 21 2019The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in quantum technologies. ... More
Liouvillian solutions for second order linear differential equations with polynomial coefficientsAug 21 2019In this paper we present an algebraic study concerning the general second order linear differential equation with polynomial coefficients. By means of Kovacic's algorithm and asymptotic iteration method we find a degree independent algebraic description ... More
Connection probabilities in the double-dimer model -- the case of two connectivity patternsAug 20 2019We apply the Grassmannian representation of the dimer model, an equivalent approach to Kasteleyn's solution to the close-packed dimer problem, to calculate the connection probabilities for the double-dimer model with wired/free/wired/free boundary conditions, ... More
Entropy in Themodynamics: from Foliation to CategorizationAug 20 2019We overview the notion of entropy in thermodynamics. We start from the smooth case using differential forms on the manifold, which is the natural language for thermodynamics. Then the axiomatic definition of entropy as ordering on set that is induced ... More
Critical Fluctuations for the Spherical Sherrington-Kirkpatrick Model in an External FieldAug 20 2019We prove the existence of a critical regime of fluctuation of the ground-state energy of the spherical Sherrington-Kirkpatrick model in an external field. Such regime was conjectured in [2,12], and occurs with external field strength $h=O(N^{-1/6})$. ... More
Holomorphic Chern-Simons theory and affine Gaudin modelsAug 20 2019We relate two formalisms recently proposed for describing classical integrable field theories. The first is based on the action of four-dimensional holomorphic Chern-Simons theory introduced and studied by Costello, Witten and Yamazaki. The second makes ... More
Colored five-vertex models and Lascoux polynomials and atomsAug 20 2019We construct an integrable colored five-vertex model whose partition function is a Lascoux atom based on the five-vertex model of Motegi and Sakai [arXiv:1305.3030] and the colored five-vertex model of Brubaker, the first author, Bump, and Gustafsson ... More
Geometry on the manifold of Gaussian quantum channelsAug 20 2019In the space of quantum channels, we establish the geometry that allows us to make statistical predictions about relative volumes of entanglement breaking channels among all the Gaussian quantum channels. The underlying metric is constructed using the ... More
Basel problem: a physicist's solutionAug 20 2019Some time ago Wastlund reformulated the Basel problem in terms of a physical system using the proportionality of the apparent brightness of a star to the inverse square of its distance. Inspired by this approach, we give another physical interpretation ... More
Minimal degenerate CSS quantum code with low cost circuitAug 20 2019Error correction is of utmost necessity for large-scale quantum computing. Quantum error correcting codes can be degenerate, if more than one type of error can map the input state to the same error state. In this paper, we propose a 6-qubit degenerate ... More
Multiple backward Schramm--Loewner evolution and coupling with Gaussian free fieldAug 20 2019It is known that a backward Schramm--Loewner evolution (SLE) is coupled with a free boundary Gaussian free field (GFF) with boundary perturbation to give a conformal welding of a quantum surface. Motivated by a generalization of conformal welding for ... More
Melonic Dominance in Subchromatic Sextic Tensor ModelsAug 20 2019We study tensor models based on $O(N)^r$ symmetry groups constructed out of rank-$r$ tensors with order-$q$ interaction vertices. We define \textit{subchromatic} tensor models to be those for which $r<q-1$. We focus most of our attention on sextic ($q=6$) ... More
Non-perturbative approaches to the quantum Seiberg-Witten curveAug 19 2019Aug 21 2019We study various non-perturbative approaches to the quantization of the Seiberg-Witten curve of ${\cal N}=2$, $SU(2)$ super Yang-Mills theory, which is closely related to the modified Mathieu operator. The first approach is based on the quantum WKB periods ... More
Non-perturbative approaches to the quantum Seiberg--Witten curveAug 19 2019We study various non-perturbative approaches to the quantization of the Seiberg-Witten curve of ${\cal N}=2$, $SU(2)$ super Yang-Mills theory, which is closely related to the modified Mathieu operator. The first approach is based on the quantum WKB periods ... More
Digraphs are different: Why directionality matters in complex systemsAug 19 2019Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect stability, percolation ... More
Fifteen-vertex models with non-symmetric $R$ matricesAug 19 2019In this work, we employ the algebraic-differential method recently developed by the author to solve the Yang-Baxter equation for arbitrary fifteen-vertex models satisfying the ice-rule. We show that there are four different families of such regular $R$ ... More
Reflection Time Difference as a probe of S-matrix Zeroes in Chaotic Resonance ScatteringAug 19 2019Motivated by recent interest in the zeroes of S-matrix entries in the complex energy plane, I use the Heidelberg model of resonance scattering to introduce the notion of Reflection Time Difference which is shown to play the same role for the {\it zeroes} ... More
Spectral determinant for the damped wave equation on an intervalAug 19 2019We evaluate the spectral determinant for the damped wave equation on an interval of length $T$ with Dirichlet boundary conditions, proving that it does not depend on the damping. This is achieved by analysing the square of the damped wave operator using ... More
Finite spectral triples for the fuzzy torusAug 19 2019Finite real spectral triples are defined to characterise the non-commutative geometry of a fuzzy torus. The geometries are the non-commutative analogues of flat tori with moduli determined by integer parameters. Each of these geometries has four different ... More
On definition of quantum tomography via the Sobolev embedding theoremAug 19 2019We obtain sufficient conditions on kernels of quantum states under which Wigner functions, optical quantum tomograms and linking their formulas are correctly defined. Our approach is based upon the Sobolev embedding theorem. The transition probability ... More
From Classical Trajectories to Quantum Commutation RelationsAug 19 2019In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian description because ... More
On symmetry and uniqueness of ground states for linear and nonlinear elliptic PDEsAug 19 2019We study ground state solutions for linear and nonlinear elliptic PDEs in $\mathbb{R}^n$ with (pseudo-)differential operators of arbitrary order. We prove a general symmetry result in the nonlinear case as well as a uniqueness result for ground states ... More
On symmetry of traveling solitary waves for dispersion generalized NLSAug 19 2019We consider dispersion generalized nonlinear Schr\"odinger equations (NLS) of the form $i \partial_t u = P(D) u - |u|^{2 \sigma} u$, where $P(D)$ denotes a (pseudo)-differential operator of arbitrary order. As a main result, we prove symmetry results ... More
Computing Spectral Measures and Spectral Types: New Algorithms and ClassificationsAug 19 2019Despite new results on computing the spectrum, there has been no general method able to compute spectral measures (as given by the classical spectral theorem) of infinite-dimensional normal operators. Given a matrix representation, we show that if each ... More
Virasoro symmetries of Drinfeld-Sokolov hierarchies and equations of Painlevé typeAug 19 2019We construct a tau cover of the generalized Drinfeld-Sokolov hierarchy associated to an arbitrary affine Kac-Moody algebra with gradations $\mathrm{s}\le\mathds{1}$ and derive its Virasoro symmetries. By imposing the Virasoro constraints we obtain solutions ... More
A CLT for the total energy of the two-dimensional critical Ising modelAug 19 2019Consider the Ising model on $([1,2N]\times[1,2M])\cap\mathbb{Z}^2$ at critical temperature with periodic boundary condition in the horizontal direction and free boundary condition in the vertical direction. Let $E_{M,N}$ be its total energy (or Hamiltonian). ... More
All tight correlation Bell inequalities have quantum violationsAug 19 2019It is by now well-established that there exist non-local games for which the best entanglement-assisted performance is not better than the best classical performance. Here we show in contrast that any two-player XOR game, for which the corresponding Bell ... More
Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) Polynomial Affine GravityAug 19 2019Starting from an affinely connected space, we consider a model of gravity whose fundamental field is the connection. We build up the action using as sole premise the invariance under diffeomorphisms, and study the consequences of a cosmological ansatz ... More
The arithmetic geometry of AdS$_2$ and its continuum limitAug 19 2019We present and study in detail the construction of a discrete and finite arithmetic geometry AdS$_2[N]$ and show that an appropriate scaling limit exists, as $N\to\infty,$ that can be identified with the universal AdS$_2$ radial and time near horizon ... More
Complexes of marked graphs in gauge theoryAug 19 2019We review the gauge graph complexes as defined by Kreimer, Sars and van Suijlekom in "Quantization of gauge fields, graph polynomials and graph homology" and compute their cohomology.
Weak-disorder limit at criticality for directed polymers on hierarchical graphsAug 19 2019We prove a distributional limit theorem conjectured in [Journal of Statistical Physics 174, No. 6, 1372-1403 (2019)] for partition functions defining models of directed polymers on diamond hierarchical graphs with disorder variables placed at the graphical ... More
On the quantum affine vertex algebra associated with trigonometric $R$-matrixAug 18 2019We apply the theory of $\phi$-coordinated modules, developed by H.-S. Li, to the Etingof--Kazhdan quantum affine vertex algebra associated with the trigonometric $R$-matrix of type $A$. We prove, for a certain associate $\phi$ of the one-dimensional additive ... More
On the multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner-Dyson symmetry classesAug 18 2019We introduce a power-law banded random matrix model for the third of the three classical Wigner-Dyson ensembles, i.e., the symplectic ensemble. A detailed analysis of the statistical properties of its eigenvectors and eigenvalues, at criticality, is presented. ... More
Geometry and integrability in $\mathcal{N}=8$ supersymmetric mechanicsAug 18 2019We construct the $\mathcal{N}=8$ supersymmetric mechanics with potential term whose configuration space is the special K\"ahler manifold of rigid type and show that it can be viewed as the K\"ahler counterpart of $\mathcal{N}=4$ mechanics related to "curved ... More
Magnetic stochasticity and diffusionAug 18 2019Aug 20 2019We develop a quantitative relationship between magnetic diffusion and the level of randomness, or stochasticity, of the diffusing magnetic field in a magnetized medium. A general mathematical formulation of magnetic stochasticity in turbulence has been ... More
Magnetic stochasticity and diffusionAug 18 2019We develop a quantitative relationship between magnetic diffusion and the level of randomness, or stochasticity, of the diffusing magnetic field in a magnetized medium. A general mathematical formulation of magnetic stochasticity in turbulence has been ... More
Quantum Mechanics of Particle on a torus knot: Curvature and Torsion EffectsAug 18 2019Constraints play an important role in dynamical systems. However, the subtle effect of constraints in quantum mechanics is not very well studied. In the present work we concentrate on the quantum dynamics of a point particle moving on a non-trivial torus ... More
Lie-Schwinger block-diagonalization and gapped quantum chains: analyticity of the ground-state energyAug 18 2019We consider quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state ... More
Lie-Schwinger block-diagonalization and gapped quantum chains with unbounded interactionsAug 18 2019We study quantum chains whose Hamiltonians are perturbations by interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state ... More
Ladders of eigenvalues and resonances in bipartite complex potentialsAug 18 2019We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large distance. We show that this operator possesses a sequence of approximately ... More
Spacing gain and absorption in a simple $\mathcal{PT}$-symmetric model: spectral singularities and ladders of eigenvalues and resonancesAug 18 2019We consider a parity-time ($\mathcal{PT}$-) symmetric waveguide consisting of a localized gain and loss elements separated by a variable distance. The situation is modelled by a Schr\"odiner operator with localized complex $\mathcal{PT}$-symmetric potential. ... More
Invariant parameterization of geostrophic eddies in the oceanAug 17 2019The framework of invariant parameterization is extended to higher-order closure schemes. We also define, for the first time, generalized invariant parameterization schemes, where symmetries of the corresponding original model are preserved as equivalence ... More
On the stability of laminar flows between platesAug 17 2019Consider a two-dimensional laminar flow between two plates, so that $(x_1,x_2)\in {\mathbb R} \times[-1,1]$, given by ${\mathbf v}(x_1,x_2)=(U(x_2),0)$, where $U\in C^4([-1,1])$ satisfies $U^\prime\neq0$ in $[-1,1]$. We prove that the flow is linearly ... More
Quasirandom quantum channelsAug 17 2019Mixing (or quasirandom) properties of the natural transition matrix associated to a graph can be quantified by its distance to the complete graph. Different mixing properties correspond to different norms to measure this distance. For dense graphs, two ... More
Ferromagnetism in the SU($n$) Hubbard model with nearly flat-bandAug 17 2019We present rigorous results for the SU($n$) Fermi-Hubbard model on a one-dimensional Tasaki lattice. We first study the model with a flat band at the bottom of the single-particle spectrum and prove that the ground states exhibit SU($n$) ferromagnetism ... More
Spectra of "fattened" open book structuresAug 17 2019We establish convergence of spectra of Neumann Laplacian in a thin neighborhood of a branching 2D structure in 3D to the spectrum of an appropriately defined operator on the structure itself. This operator is a 2D analog of the well known by now quantum ... More
From deterministic dynamics to thermodynamic laws II: Fourier's law and mesoscopic limit equationAug 17 2019This paper consider the mesoscopic limit of a stochastic energy exchange model that is numerically derived from deterministic dynamics. The law of large numbers and the central limit theorems are proved. We show that the limit of the stochastic energy ... More
A Shift Selection Strategy for Parallel Shift-Invert Spectrum Slicing in Symmetric Self-Consistent Eigenvalue ComputationAug 16 2019The central importance of large scale eigenvalue problems in scientific computation necessitates the development massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of ... More
Quantum geometry from higher gauge theoryAug 16 2019Higher gauge theories play a prominent role in the construction of 4d topological invariants and have been long ago proposed as a tool for 4d quantum gravity. The Yetter lattice model and its continuum counterpart, the BFCG theory, generalize BF theory ... More
Iterated $φ^4$ KinksAug 16 2019A first order equation for a static ${\phi}^4$ kink in the presence of an impurity is extended into an iterative scheme. At the first iteration, the solution is the standard kink, but at the second iteration the kink impurity generates a kink-antikink ... More
Matrix Lie Maps and Neural Networks for Solving Differential EquationsAug 16 2019The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It can be used ... More
Brownian Loops, Layering Fields and Imaginary Gaussian Multiplicative ChaosAug 16 2019We study vertex-like operators built from the Brownian loop soup in the limit as the loop soup intensity tends to infinity. More precisely, following Camia, Gandolfi and Kleban (Nuclear Physics B 902, 2016), we take a Brownian loop soup in a planar domain ... More
A toolkit for twisted chiral superfieldsAug 16 2019We calculate the most general terms for arbitrary Lagrangians of twisted chiral superfields in 2D (2,2) supersymmetric theories [1]. The scalar and fermion kinetic terms and interactions are given explicitly. We define a set of twisted superspace coordinates, ... More
Poisson vertex algebras in supersymmetric field theoriesAug 15 2019A large class of supersymmetric quantum field theories, including all theories with $\mathcal{N} = 2$ supersymmetry in three dimensions and theories with $\mathcal{N} = 2$ supersymmetry in four dimensions, possess topological-holomorphic sectors. We formulate ... More
Arctic curve of the free-fermion six-vertex model with reflecting end boundary conditionAug 15 2019We consider the six-vertex model with reflecting end boundary condition. We study the asymptotic behavior of the boundary correlations. This asymptotic behavior is used as an input into the Tangent Method in order to derive analytically the arctic curve ... More
Boundary-to-bulk maps for AdS causal wedges and RG flowAug 15 2019We consider the problem of defining spacelike-supported boundary-to-bulk propagators in AdS$_{d+1}$ down to the unitary bound $\Delta=(d-2)/2$. That is to say, we construct the `smearing functions' $K$ of HKLL but with different boundary conditions where ... More
Large n limit for the product of two coupled random matricesAug 15 2019For a pair of coupled rectangular random matrices we consider the squared singular values of their product, which form a determinantal point process. We show that the limiting mean distribution of these squared singular values is described by the second ... More
From Short-Range to Contact Interactions in the 1d Bose GasAug 15 2019For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by Schr\"odinger operators ... More
Dissipative generators, divisible dynamical maps and Kadison-Schwarz inequalityAug 15 2019We introduce a concept of Kadison-Schwarz divisible dynamical maps. It turns out that it is a natural generalization of the well known CP-divisibility which characterizes quantum Markovian evolution. It is proved that Kadison-Schwarz divisible maps are ... More
Sharp polynomial decay rates for the damped wave equation with Hölder-like dampingAug 15 2019We study decay rates for the energy of solutions of the damped wave equation on the torus. We consider dampings invariant in one direction and bounded above and below by multiples of $x^{\beta}$ near the boundary of the support and show decay at rate ... More
Random surfaces and Liouville quantum gravityAug 15 2019Liouville quantum gravity (LQG) surfaces are a family of random fractal surfaces which can be thought of as the canonical models of random two-dimensional Riemannian manifolds, in the same sense that Brownian motion is the canonical model of a random ... More
Algebraic Coarse-Graining of Biochemical Reaction NetworksAug 15 2019Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive coarse-graining ... More
Strong Scott ConjectureAug 15 2019In heavy atoms and molecules, on the distances $\lesssim Z_m^{-1}$ from one of the nuclei (with a charge $Z_m$) we prove that $\rho_\Psi (x)$ is approximated in $L^1$-norm with the relative error $\ll Z_m^{-1/15}$ by the electronic density for a single ... More
Conjugated equilibrium solutions for the $2$--body problem in the two dimensional sphere $\mathbb{M}^2_R$ for equal massesAug 14 2019We study here the behaviour of solutions for conjugated (antipodal) points in the $2$-body problem on the two-dimensional sphere $\mathbb{M}^2_R$. We use a slight modification of the classical potential used commonly in \cite{Borisov}, \cite{Diacu} and ... More
Cooperative metabolic resource allocation in spatially-structured systemsAug 14 2019This paper extends a framework for dynamic metabolic resource allocation based on the maximum entropy principle to spatiotemporal models of metabolism with cooperation. Much like the maximum entropy principle encapsulates `bet-hedging' behaviour displayed ... More
Many-Body Localization LandscapeAug 14 2019We generalize the notion of "localization landscape," introduced by M. Filoche and S. Mayboroda [Proc. Natl. Acad. Sci. USA 109, 14761 (2012)] for the single-particle Schrodinger operator, to a wide class of interacting many-body Hamiltonians. The many-body ... More
Global Symmetry and Maximal ChaosAug 14 2019In this note we study chaos in generic quantum systems with a global symmetry generalizing seminal work [arXiv : 1503.01409] by Maldacena, Shenker and Stanford. We conjecture a bound on chaos exponent in a thermodynamic ensemble at temperature $T$ and ... More
On Hamiltonians for Kerov functionsAug 14 2019Kerov Hamiltonians are defined as a set of commuting operators which have Kerov functions as common eigenfunctions. In the particular case of Macdonald polynomials, well known are the exponential Ruijsenaars Hamiltonians, but the exponential shape is ... More
The sum-of-squares hierarchy on the sphere, and applications in quantum information theoryAug 14 2019We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of Sum-of-Squares (SOS) relaxations. Exploiting the polynomial kernel technique, we obtain a quadratic improvement of the known convergence rate by Reznick ... More
A note about fractional Stefan problemAug 14 2019We derive the fractional version of one-phase one-dimensional Stefan model. We assume that the diffusive flux is given by the time-fractional Riemann-Liouville derivative, i.e. we impose the memory effect in the examined model.
Soliton solutions of the nonlinear Schrödinger equation with defect conditionsAug 14 2019A recent development in the derivation of soliton solutions for initial-boundary value problems through Darboux transformations motivated us to reconsider solutions to the nonlinear Schr\"odinger equation on two half-lines connected via integrable defect ... More
Determination of isometric real-analytic metric and spectral invariants for elastic Dirichlet-to-Neumann map on Riemannian manifoldsAug 14 2019For a compact Riemannian manifold $(\Omega, g)$ with smooth boundary $\partial \Omega$, we explicitly give local representation and full symbol expression for the elastic Dirichlet-to-Neumann map $\Xi_g$ by factorizing an equivalent elastic equation. ... More
Quantum Systems at The Brink. Existence and Decay Rates of Bound States at Thresholds; AtomsAug 14 2019It is well known that $N$-electron atoms undergoes unbinding for a critical charge of the nucleus $Z_c$, i.e. the atom has eigenstates for the case $Z> Z_c$ and it has no bound states for $Z<Z_c$. In the present paper we derive upper bound for the bound ... More
Cylindrically symmetric $n$-dimensional (un)charged de Sitter and anti-de Sitter black holes in generic $f(T)$ gravityAug 14 2019Given a generic function $f(T)$ we construct in almost closed forms cylindrically symmetric $n$-dimensional uncharged and charged de Sitter and anti-de Sitter solutions (including black holes, wormholes and possibly other regular solutions) in $f(T)$ ... More
Matrix composition via Rolling ConesAug 14 2019Louis Poinsot has shown in 1854 that the motion of a rigid body, with one of its points fixed, can be described as the rolling without slipping of one cone, the 'body cone', along another, the 'space cone', with their common vertex at the fixed point. ... More
Linear Differential Equations for the Resolvents of the Classical Matrix EnsemblesAug 14 2019The spectral density for random matrix $\beta$ ensembles can be written in terms of the average of the absolute value of the characteristic polynomial raised to the power of $\beta$, which for even $\beta$ is a polynomial of degree $\beta(N-1)$. In the ... More
Taking a Lesson from Quantum Particles for Statistical Data PrivacyAug 14 2019Privacy is under threat from artificial intelligence revolution fueled by unprecedented abundance of data. Differential privacy, an established candidate for privacy protection, is susceptible to adversarial attacks, acts conservatively, and leads to ... More
3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzlesAug 14 2019We establish the stability of 3-D axisymmetric transonic shock solutions of the steady full Euler system in divergent nozzles under small perturbations of an incoming radial supersonic flow and a constant pressure at the exit of the nozzles. To study ... More
3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzlesAug 14 2019Aug 15 2019We establish the stability of 3-D axisymmetric transonic shock solutions of the steady full Euler system in divergent nozzles under small perturbations of an incoming radial supersonic flow and a constant pressure at the exit of the nozzles. To study ... More
Quantum Elliptic Calogero-Moser Systems from Gauge OrigamiAug 14 2019We systematically study the interesting relations between the quantum elliptic Calogero-Moser system (eCM) and its generalization, and their corresponding supersymmetric gauge theories. In particular, we construct the suitable characteristic polynomial ... More
Quantum Systems at The Brink. Existence and Decay Rates of Bound States at Thresholds; HeliumAug 13 2019Existence and decay rates of eigenfunctions for Schr\"odinger operators provide interesting and important questions in quantum mechanics. It is well known that for eigenvalues below the threshold of the essential spectrum eigenvectors exist and decay ... More