Related papers: QKZ-Ruijsenaars correspondence revisited
The gl(N) and U_q(gl(N)) quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matrices…
These notes summarize a set of lectures on phenomenological quantum gravity which one of us delivered and the other attended with great diligence. They cover an assortment of topics on the border between theoretical quantum gravity and…
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless…
In order to extend the geometrization of Yangian $R$-matrices from Lie algebras $gl(n)$ to superalgebras $gl(M|N)$, we introduce new quiver-related varieties which are associated with representations of $gl(M|N)$. In order to define them…
This is the first in a two-part series in which we extend non-relativistic stochastic mechanics, in the ZSM formulation [1, 2], to semiclassical Newtonian gravity (ZSM-Newton) and semiclassical Newtonian electrodynamics (ZSM-Coulomb), under…
General algebraic properties of the algebras of vector fields over quantum linear groups $GL_q(N)$ and $SL_q(N)$ are studied. These quantum algebras appears to be quite similar to the classical matrix algebra. In particular, quantum…
The recovery of classical chaotic dynamics from quantum systems has long been a subject of interest. Furthermore, recent work indicates that quantum chaos may well be significant in quantum information processing. In this paper we discuss…
Causality constrains the gravitational interactions of massive higher spin particles in both AdS and flat spacetime. We explore the extent to which these constraints apply to composite particles, explaining why they do not rule out…
In this paper we study the Brauer loop model on a strip and the associated quantum Knizhnik--Zamolodchikov (qKZ) equation. We show that the minimal degree solution of the Brauer qKZ equation with one of four different possible boundary…
We consider semiclassically scaled, weakly nonlinear Schr\"odinger equations with external confining potentials and additional angular-momentum rotation term. This type of model arises in the Gross-Pitaevskii theory of trapped, rotating…
Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this gives the q-deformed Poisson brackets in terms…
Bianchi -I, -III, and FRW type models minimally coupled to a massive spatially homogeneous scalar field (i.e. a particle) are studied in the framework of semiclassical quantum gravity. In a first step we discuss the solutions of the…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
We simulated spin-spin interactions of $N$-bodies in linearized General Relativity (GR) and linearized Massive Gravity of the Fierz-Pauli type (mGR). It was noted earlier that there is a discrete difference between the spin-spin interaction…
Braneworld scenarios are motivated by string/M-theory and can be characterized by the way in which they modify the conventional Friedmann equations of Einstein gravity. An alternative approach to quantum gravity, however, is the loop…
We use a nonlinear Schroedinger-Poisson equation to describe two interacting electrons with opposite spins confined in a parabolic potential, a quantum dot. We propose an effective form of the Poisson equation taking into account the…
We study caustics in classical and quantum mechanics for systems with quadratic Lagrangians. We derive a closed form of the transition amplitude on caustics and discuss their physical implications in the Gaussian slit (gedanken-)experiment.…
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of…
We compare the quantum and classical properties of the (Quantum) Isoperiodic Stable Structures -- (Q)ISSs -- which organize the parameter space of a paradigmatic dissipative ratchet model, i.e. the dissipative modified kicked rotator. We…
This paper discusses the somewhat unintuitive conjecture that many Lorentz-invariant many-particle models can be reinterpreted to satisfy the gtr field equations. It is shown that a careful remapping of coordinates yields a non-trivial…