Related papers: Generalized statistics in one dimension
Generalized quantum statistics, such as paraboson and parafermion statistics, are characterized by triple relations which are related to Lie (super)algebras of type B. The correspondence of the Fock spaces of parabosons, parafermions as…
We introduce and discuss Monte Carlo methods in quantum field theories. Methods of independent Monte Carlo, such as random sampling and importance sampling, and methods of dependent Monte Carlo, such as Metropolis sampling and Hamiltonian…
One-dimensional fractional statistics is studied using the Calogero-Sutherland model (CSM) which describes a system of non-relativistic quantum particles interacting with inverse-square two-body potential on a ring. The inverse-square…
We provide a complete and exact quantum description of coherent light scattering in a one-dimensional multi-mode transmission line coupled to a two-level emitter. Using recently developed scattering approach we discuss transmission…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
For nonautonomous Hamiltonian systems and their quantisations we discuss properties of the quantised systems, related to those of the corresponding classical systems, described by the KAM-related theories: the proper KAM, the averaging…
In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which are the…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the…
I give a concise introduction to some essential concepts of statistical mechanics: 1. Probability theory (constrained distributions, concentration theorem, frequency estimation, hypothesis testing); 2. Macroscopic systems in equilibrium…
A scheme based on a unifying q-deformed algebra and associated with a generalized Lax operator is proposed for generating integrable quantum and statistical models. As important applications we derive known as well as novel quantum models…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
We introduce and motivate the study of quantum spin chains on a one-dimensional lattice. We classify the varieties of methods that have been used to study these models into three categories, - a) exact methods to study specific models b)…
We present a historical review of anyon and exclusion statistics, introduced in the 1980s and 1990s respectively, and then turn to developments in the recently introduced inclusion statistics. In contrast to exclusion statistics, where…
General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible…
Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…
The existence of intimate relation between generalized statistics and supersymmetry is established by observation of hidden supersymmetric structure in pure parabosonic systems. This structure is characterized generally by a nonlinear…
Contents: 1.- Introduction 2.- Scaling of entanglement in (1+1)-dimensional systems 3.- Entanglement and RG-flows 4.- Matrix Product States Appendix A.- Entanglement and order relations B.- Hilbert space in a conformal theory
We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…