Related papers: Particles versus fields in PT-symmetrically deform…
For the models of $N$-body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent parameters into that of unit spring constant and unit mass of…
Dynamical systems exhibiting both PT and Supersymmetry are analyzed in a general scenario. It is found that, in an appropriate parameter domain, the ground state may or may not respect PT-symmetry. Interestingly, in the domain where…
Integrable structures arise in general relativity when the spacetime possesses a pair of commuting Killing vectors admitting 2-spaces orthogonal to the group orbits. The physical interpretation of such spacetimes depends on the norm of the…
We discuss a PT-symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schr\"{o}dinger equation for a particle in a square box with the PT-symmetric potential $V(x,y)=iaxy$. Perturbation theory clearly shows that…
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2) supersymmetry. Several results related to exactly…
We present a construction of $\kappa$-deformed complex scalar field theory with the objective of shedding light on the way discrete symmetries and CPT invariance are affected by the deformation. Our starting point is the observation that,…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
On the example of a real scalar field, an approach to quantization of non-linear fields and construction of the perturbation theory with account of spontaneous symmetry breaking is proposed. The method is based on using as the main…
A Parity-Time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrodinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is…
Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field…
We suggest that trialgebraic symmetries migth be a sensible starting point for a notion of integrability for two dimensional spin systems. For a simple trialgebraic symmetry we give an explicit condition in terms of matrices which a…
A moving parallel frame method is applied to geometric non-stretching curve flows in the Hermitian symmetric space Sp(n)/U(n) to derive new integrable systems with unitary invariance. These systems consist of a bi-Hamiltonian modified…
We consider the interaction of a ferromagnetic spinor Bose-Einstein condensate with a magnetic field gradient. The magnetic field gradient realizes a spin-position coupling that explicitly breaks time-reversal symmetry T and space parity P,…
Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is…
A connection between integrable quantum field theory and the spectral theory of ordinary differential equations is reviewed, with particular emphasis being given to its relevance to certain problems in PT-symmetric quantum mechanics.
The rational Calogero model based on an arbitrary rank-$n$ Coxeter root system is spherically reduced to a superintegrable angular model of a particle moving on $S^{n-1}$ subject to a very particular potential singular at the reflection…
Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…
We demonstrate that a coherently-prepared four-level atomic medium can provide a versatile platform for realizing parity-time (PT) symmetric optical potentials. Different types of PT-symmetric potentials are proposed by appropriately tuning…