Related papers: The $\mathrm{GL}_n$-Connes-Marcolli Systems
Maximally entangled states should maximally violate the Bell inequality. In this paper, it is proved that all two-qubit states that maximally violate the Bell-Clauser-Horne-Shimony-Holt inequality are exactly Bell states and the states…
We present a minimally entangled typical thermal state (METTS) quantum impurity solver for general multi-orbital systems at finite temperatures. We introduce an improved estimator for the single-particle Green's function that strongly…
The Eigenstate Thermalization Hypothesis implies that for a thermodynamically large system in one of its eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of {\it relevant} conserved…
The interpolation method for mean field spin glass models developed by Guerra and Talagrand is extended to a quantum mean field spin glass model. This extension enables us to obtain both replica-symmetric (RS) and one step replica-symmetry…
We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical…
It is known that each single typical pure state in an energy shell of a large isolated quantum system well represents a thermal equilibrium state of the system. We show that such typicality holds also for nonequilibrium steady states…
Thermalization of isolated quantum systems is a long-standing fundamental problem where different mechanisms are proposed over time. We contribute to this discussion by classifying the diverse quench dynamical behaviours of spin-1…
Non-equilibrium steady states (NESS) describe particularly simple and stationary non-equilibrium situations. A possibility to obtain such states is to consider the asymptotic evolution of two infinite heat baths brought into thermal…
In many quantum quench experiments involving cold atom systems the post-quench system can be described by a quantum field theory of free scalars or fermions, typically in a box or in an external potential. We work with free scalars in…
The Kohn-Sham (KS) equations determine, in a self-consistent way, the particle density of an interacting fermion system at thermal equilibrium. We consider a situation when the KS equations are known to have a unique solution at high…
We examine n component spin systems with arbitrary two spin interactions (of unspecified range) within a general framework to highlight some new subtleties present in incommensurate systems. We determine the ground states of all…
A unified (classical-quantum-statistical) formalism for a system with continuous spectrum is introduced. For this kind of systems ergodicity behavior and the existence of microcanonical and canonical (KMS) equilibrium is proved. It is…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
We extend the formalism of pure state thermodynamics to matrix product states. In pure state thermodynamics finite temperature properties of quantum systems are derived without the need of statistical mechanics ensembles, but instead using…
This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which…
The problem of temperature in nonextensive statistical mechanics is studied. Considering the first law of thermodynamics and a "quasi-reversible process", it is shown that the Tsallis entropy becomes the Clausius entropy if the inverse of…
We show that the recently discovered thermodynamic equivalence between noninteracting Bose and Fermi gases in two dimensions, and between one-dimensional Bose and Fermi systems with linear dispersion, both in the grand-canonical ensemble,…
These lectures introduce techniques that are used in the description of systems of particles and fields at high temperature (or density). These methods have a broad range of physical applications. We shall discuss two specific applications:…
The reduced density matrices (RDMs) are calculated in the thermodynamic limit for the Chern-Simons non-relativistic particle system and Maxwell-Boltzmann (MB) statistics. It is established that they are zero outside of a diagonal and…
The local converse theorem for Rankin-Selberg gamma factors of $\mathrm{GL}_2(\mathbb{F}_q)$ proved by Piatetski-Shapiro over $\mathbb{C}$ no longer holds after reduction modulo $\ell \neq p$. To remedy this, we construct new $\mathrm{GL}_n…