相关论文: Quasi-Exactly-Solvable Many-Body Problems
In this paper we prove the multiplicity of solutions for a class of quasilinear problems in $ \mathbb{R}^{N} $ involving variable exponents. The main tool used is in the proof are the direct methods, Ekeland's variational principle and some…
We consider the $n$--body problem defined on surfaces of constant negative curvature. For the case of $n$--equal masses we prove that the hyperbolic relative equilibria with a regular polygonal shape do not exist. In particular the…
The hyperbolic Lie algebras with symmetrizable Cartan matrix are classified, there are 142 of them some of which can be ``superized'' to an almost affine Lie superalgebra. We list all 97 pairs (a hyperbolic Lie algebra $H$, its superized…
Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lam\'e polynomials of arbitrary order. The models discussed are…
We show that the thermodynamic limit of a many-body system can reveal entanglement properties that are hard to detect in finite-size systems -- similar to how phase transitions only sharply emerge in the thermodynamic limit. The resulting…
Symmetries play a crucial role in understanding phases of matter and the transitions between them. Theoretical investigations of quantum models with SU($N$) symmetry have provided important insights into many-body phenomena. However, these…
Quantum many-body scars provide a controlled form of weak ergodicity breaking, in which structured nonthermal eigenstates coexist with a thermalizing many-body spectrum. We introduce a qubit-level route to exact scars based on the intrinsic…
In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of…
The algebra of observables of an N-body Calogero model is represented on the S_N-symmetric subspace of the positive definite Fock space. We discuss some general properties of the algebra and construct four different realizations of the…
Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles…
General reduction of the elliptic hypergeometric equation to the level of complex hypergeometric functions is described. The derived equation is generalized to the Hamiltonian eigenvalue problem for new rational integrable $N$-body systems…
A second-order differential (q-difference) eigenvalue equation is constructed whose solutions are generating functions of the dual (q-)Hahn polynomials. The fact is noticed that these generating functions are reduced to the (little…
General properties of the three-body problem in a model of modified dynamics are investigated. It is shown that the three-body problem in this model shares some characters with the similar problem in Newtonian dynamics. Moreover, the planar…
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…
Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing…
Quasi-Boolean algebras were introduced as the generalization of Boolean algebras in the setting of quantum computation logic. In this paper, we investigate the completeness and congruences of quasi-Boolean algebras. First, we discuss the…
A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion ("acceleration equal force") featuring one-body and two-body velocity-dependent forces "of goldfish type" which determine the…
Although rare, collisions of two or more bodies in the N-body problem are apparent obstacles at which Newton's Law of Gravity ceases to make sense. Without understanding the nature of collisions, a complete understanding of the N-body…
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…
Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and…