相关论文: Understanding Permutation Symmetry
Identical particles exhibit correlations even in the absence of inter-particle interaction, due to the exchange (anti)symmetry of the many-particle wavefunction. Two fermions obey the Pauli principle and anti-bunch, whereas two bosons favor…
The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two…
The Ising model is the simplest to describe many-body effects in classical statistical mechanics. Duality analysis leads to a critical point under several assumptions. The Ising model itself has $Z(2)$ symmetry. The basis of the duality…
This paper focuses on the size-biased permutation of $n$ independent and identically distributed (i.i.d.) positive random variables. This is a finite dimensional analogue of the size-biased permutation of ranked jumps of a subordinator…
We build on the foundational work of Deffner and Zurek [S. Deffner and W. H. Zurek, New J. Phys. 18, 063013 (2016)] to show how central equilibrium structures of statistical mechanics can be understood within standard quantum mechanics…
Spontaneous symmetry breaking is a cornerstone of modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous…
The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate…
Any permutation statistic $f:\sym\to\CC$ may be represented uniquely as a, possibly infinite, linear combination of (classical) permutation patterns: $f= \Sigma_\tau\lambda_f(\tau)\tau$. To provide explicit expansions for certain…
A permutation on an alphabet $ \Sigma $, is a sequence where every element in $ \Sigma $ occurs precisely once. Given a permutation $ \pi $= ($\pi_{1} $, $ \pi_{2} $, $ \pi_{3} $,....., $ \pi_{n} $) over the alphabet $ \Sigma $ =$\{ $0, 1,…
Within the theory of statistical ensemble, the so-called $\mu PT$ ensemble describes equilibrium systems that exchange energy, particles, and volume with the surrounding. General, model-independent features of volume and particle number…
Non-hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce, leading to a non-diagonalizable Jordan block. It is known that symmetries can enhance the abundance of…
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…
Progress in the reliable preparation, coherent propagation and efficient detection of many-body states has recently brought collective quantum phenomena of many identical particles into the spotlight. This tutorial introduces the physics of…
This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify…
Despite the obvious difference between fermions and bosons in their physical properties and statistical distributions, but we have to ask the following question. What is the form of statistical distribution for a system of quantum particles…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge)…
Second-order phase transitions have no latent heat and are characterized by a change in symmetry. In addition to the conventional symmetric and anti-symmetric states under permutations of bosons and fermions, mathematical…
Topological order in two dimensions can be described in terms of deconfined quasiparticle excitations - anyons - and their braiding statistics. However, it has recently been realized that this data does not completely describe the situation…
Preservation of coherence is a fundamental yet subtle phenomenon in open systems. We uncover its relation to symmetries respected by the system Hamiltonian and its coupling to the environment. We discriminate between local and global…