Related papers: Generating functions for canonical systems of ferm…
We derive exact relations for $N$ spin-1/2 fermions with zero-range or short-range interactions, in continuous space or on a lattice, in $2D$ or in $3D$, in any external potential. Some of them generalize known relations between energy,…
We present a symbolic implementation of recursion method for the dynamics of strongly correlated fermions on one-, two- and three-dimensional lattices. Focusing on two paradigmatic models, interacting spinless fermions and the Hubbard…
The derivation of electromagnetic gyrofluid equations is made systematic by using the Hermite polynomial form of the underlying delta-f gyrokinetic distribution function. The gyrokinetic free-energy functional is explicitly used to set up…
We have developed an efficient simulation algorithm for strongly interacting relativistic fermions in two-dimensional field theories based on a formulation as a loop gas. The loop models describing the dynamics of the fermions can be mapped…
In this paper, we introduce a new method for computing generating functions with respect to the number of descents and left-to-right minima over the set of permutations which have no consecutive occurrences of a pattern that starts with 1.
Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy…
We consider two different physical systems for which the basis of the Hilbert space can be parametrized by Young diagrams: free complex fermions and the phase model of strongly correlated bosons. Both systems have natural, well-known…
We obtain, for a subclass of structure functions characterizing a first class Hamiltonian system, recursive relations from which the general form of the local symmetry transformations can be constructed in terms of the independent gauge…
We analyze the universality of the bosonization rules in non-relativistic fermionic systems in $(2+1)d$. We show that, in the case of linear fermionic dispersion relations, a general fermionic theory can be mapped into a gauge theory in…
We investigate a number of semantically defined fragments of Tarski's algebra of binary relations, including the function-preserving fragment. We address the question whether they are generated by a finite set of operations. We obtain…
The free energy of a multi-component scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys non-linear functional differential equations which are turned into…
We present a classical simulation method for fermionic quantum systems which, without loss of generality, can be represented by parity-preserving circuits made of two-qubit gates in a brick-wall structure. We map such circuits to a…
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…
We propose an interaction flow scheme that sums up the perturbation expansion of many-particle systems by successively increasing the interaction strength. It combines the unbiasedness of renormalization group methods with the simplicity of…
Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum…
This paper studies mathematical properties of reaction systems that was introduced by Enrenfeucht and Rozenberg as computational models inspired by biochemical reaction in the living cells. In particular, we continue the study on the…
We introduce high-energy limits which allow us to derive recursion relations fixing the various couplings of Lagrangians of two-dimensional relativistic quantum field theories with no tree-level particle production in a very straightforward…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…
In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales…
We develop recursion relations, in particle number, for all (unprojected) Jain composite fermion (CF) wave functions. These recursions generalize a similar recursion originally written down by Read for Laughlin states, in mixed first-second…