Related papers: General criterion for harmonicity
We present a novel class of real symmetric matrices in arbitrary dimension $d$, linearly dependent on a parameter $x$. The matrix elements satisfy a set of nontrivial constraints that arise from asking for commutation of pairs of such…
The dynamics of BCS (Bardeen-Cooper-Schrieffer) superconductors is fairly well understood due to the availability of a mean field solution for the pairing Hamiltonian, a solution which gives the quantum state of superconductor as a state of…
Usual separability criteria applicable to distinguishable particles are not applicable to identical particles. Here we show that Partial transposition and symmetrization (or anti symmetrization) of density matrix of bipartite boson systems…
We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer…
A real persymmetric Jacobi matrix of order $n$ whose eigenvalues are $2k^2$ $(k=0, ..., n-1)$ is presented, with entries given as explicit functions of $n$. Besides the possible use for testing forward and inverse numerical algorithms, such…
The free energies of six-vertex models on general domain D with various boundary conditions are investigated with the use of the n-equivalence relation which classifies the thermodynamic limit properties. It is derived that the free energy…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
We establish a unified theoretical framework that connects classical orthogonal polynomial systems to matrix Lyapunov equations through the fundamental physics of energy dissipation in stochastic dynamical systems. Starting from the energy…
We obtain the explicit rate of convergence $N^{-1/2 + \epsilon}$ for the gaps of generalized Wigner matrices in the bulk of the spectrum, for distributions of matrix entries possibly atomic and supported on enough points. The proof proceeds…
Using the example of the SU(2) gauge theory in 3+1 dimensions we consider the construction of a 3-dimensional effective model in terms of Polyakov loops. We demonstrate the application of an equilibrium self-consistency condition to the…
The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…
A parameter method is introduced in order to estimate the relationship among the various variables of a system in equilibrium, where the potential energy functions are incompletely known or the quantum mechanical calculations very…
Employing a classical density-functional description of liquid environments, we introduce a rigorous method for the diffusion quantum Monte Carlo calculation of free energies and thermodynamic averages of solvated systems that requires…
We extend the Langevin dynamics so that particles can be exchanged with a particle reservoir. We show that grand canonical ensembles are realized at equilibrium and derive the relations of thermodynamics for processes between equilibrium…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
We formulate the accuracy of quantum measurement for a qubit system in terms of a 3 by 3 matrix. This matrix, which we refer to as the accuracy matrix, can be calculated from a positive operator-valued measure (POVM) corresponding to the…
The paper presents efficient approaches for evaluating convergence rate in total variation for finite and general linear Markov chains. The motivation for studying convergence rate in this metric is its usefulness in various limit theorems.…
In a recent work we have proposed an original analytic expression for the partition function of the quartic oscillator. This partition function, which has a simple and compact form with {\it no adjustable parameters}, reproduces some key…
General physical background of Peres-Horodecki positive partial transpose (ppt-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to the "local causality reversal"…
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…