Related papers: Statistical Phases and Momentum Spacings for One-D…
We argue, based on general principles, that topological order is essential to realize fractionalization in gapped insulating phases in dimensions $d \geq 2$. In $d=2$ with genus $g$, we derive the existence of the minimum topological…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
Exchange statistics are a fundamental principle of quantum mechanics, dictating the symmetry of identical particle wavefunctions and thereby enabling emergent phenomena of many-body quantum states. The exchange-induced unitary…
Anyons are exotic quasi-particles with fractional charge that can emerge as fundamental excitations of strongly interacting topological quantum phases of matter. Unlike ordinary fermions and bosons, they may obey non-abelian statistics--a…
Microcanonical statistics can be well applied to non-extensive systems like nuclei, atomic clusters and systems at phase transitions of first order with inhomogeneous configurations like phase separation. No thermodynamic limit has to be…
I discuss the concept of fractional exclusion statistics (FES) and I show that in order to preserve the thermodynamic consistency of the formalism, the exclusion statistics parameters should change if the species of particles in the system…
We investigate non-equilibrium phase coexistence associated with a first-order phase transition by numerically studying a one-dimensional Hamiltonian-Potts model with fractional spatial derivatives. The fractional derivative is introduced…
The frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency independent…
Statistical mechanics has grown without bounds in space. Statistical mechanics of point particles in an unbounded perfect gas is commonly accepted as a foundation for understanding many systems, including liquids like the concentrated salt…
An analogy between the twisted quantum xxz model and a gated Josephson junction array is used to predict sharp structure in the critical currents versus gate voltage, and fractional AC Josephson frequencies. We prove selection rules for…
In the present work we explore features of single and pairs of solitary waves in a fractional variant of the nonlinear Schr{\"o}dinger equation. Motivated by the recent experimental realization of arbitrary fractional exponents, upon…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
Under the separability assumption on the augmented density, a distribution function can be always constructed for a spherical population with the specified density and anisotropy profile. Then, a question arises, under what conditions the…
A non-abelian anyon can only occur in the presence of ground state degeneracy in the plane. It is conceivable that for some strange anyon with quantum dimension $>1$ that the resulting representations of all $n$-strand braid groups $B_n$…
The fractional moment method, which was initially developed in the discrete context for the analysis of the localization properties of lattice random operators, is extended to apply to random Schr\"odinger operators in the continuum. One of…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
For characterizing the Brownian motion in a bounded domain: $\Omega$, it is well-known that the boundary conditions of the classical diffusion equation just rely on the given information of the solution along the boundary of a domain; on…
Unconventional quasiparticles emerging in the fractional quantum Hall regime present the challenge of observing their exotic properties unambiguously. Although the fractional charge of quasiparticles has been demonstrated since nearly three…
The thermodynamic distribution function for exclusion statistics is derived. Creation and annihilation operators for particles obeying such statistics are discussed. A connection with anyons is pointed out.
Modern statistical thermodynamics retains the concepts employed by Landau of the order parameter and a functional depending on it, now called the Hamiltonian. The present paper investigates the limits of validity for the use of the…