相关论文: Calogero-like model without rearrangement symmetry

The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of…

The entanglement dynamics in a non-Hermitian quantum system is studied numerically and analyzed from the viewpoint of quasiparticle picture. As a concrete model, we consider a one-dimensional tight-binding model with asymmetric hopping…

In the two preceding parts of this series of papers, we introduced and studied a recursion scheme for constructing joint eigenfunctions $J_N(a_+, a_-,b;x,y)$ of the Hamiltonians arising in the integrable $N$-particle systems of hyperbolic…

Artificial neural networks have been recently introduced as a general ansatz to compactly represent many- body wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamil- tonian ground states and…

We introduce a quantum generalization of classical kinetic Ising models, described by a certain class of quantum many body master equations. Similarly to kinetic Ising models with detailed balance that are equivalent to certain Hamiltonian…

Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. In…

The Calogero model bears, in the continuum limit, collective excitations in the form of density waves and solitary modulations of the density of particles. This sector of the spectrum of the model was investigated, mostly within the…

We determine the complete structure of the symmetry algebras associated with the N-body Calogero-Moser system and its maximally superintegrable discretization. We prove that the discretization naturally leads to a nontrivial deformation of…

We study "the Caged Anisotropic Harmonic Oscillator", which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n), but…

The potential of the $A_2$ quantum elliptic model (3-body Calogero-Moser elliptic model) is defined by the pairwise three-body interaction through Weierstrass $\wp$-function and has a single coupling constant. A change of variables has been…

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…

Starting from the Hamiltonian formulation of ${\cal N}{=}\,2$ supersymmetric Calogero models associated with the classical $A_n, B_n, C_n$ and $D_n$ series and their hyperbolic/trigonometric cousins, we provide their superspace description.…

I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system…

In 2+1 dimensions, we propose a renormalizable non-linear sigma model action which describes the $\mathcal{N}=2$ supersymmetric generalization of Galilean Electrodynamics. We first start with the simplest model obtained by null reduction of…

We have recently extended many-body perturbation theory and coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the restoration of the angular momentum at any truncation order [T.…

For any central potential V in D dimensions, the angular Schroedinger equation remains the same and defines the so called hyperspherical harmonics. For non-central models, the situation is more complicated. We contemplate two examples in…

We reconsider the generalization of standard quantum mechanics in which the position operators do not commute. We argue that the standard formalism found in the literature leads to theories that do not share the symmetries present in the…

We investigate the ground state properties of a family of $N$-body systems in 1-dimension, trapped in a polynomial potential and having long range 2-body interaction in addition to the inverse square potential studied in the…

Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…

We first present a consistent canonical formulation of the general (non-marginal) Oppenheimer-Snyder model. The switching between comoving and stationary observer is achieved by promoting coordinate transformations between dust proper time…