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Resonance and decay phenomena are ubiquitous in the quantum world. To understand them in their complexity it is useful to study solvable models in a wide sense, that is, systems which can be treated by analytical means. The present review…
In this work, a possible description for quantum dynamics of the cuscuton within the sigma-model approach is presented. Lower order perturbative corrections and the structure of divergences are found. Motivated by the results generated by…
I show how the Fermi and Bose pressures in quantum systems, identified in standard discussions through the use of thermodynamic analogies, can be derived directly in terms of the flow of momentum across a surface by using the quantum…
Effects due to fermion-vacuum polarization by an external static magnetic field are considered in a two-dimensional noncompact curved space with a nontrivial topology. An expression for the vacuun angular momentum is obtained. Like the…
An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical…
We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for…
Instanton analysis is applied to models B--H of critical dynamics. It is shown that the static instanton of the massless $\phi^{4}$ model determines the large-order asymptotes of the perturbation expansion of these near-equilibrium dynamic…
Topological phases of matter are one of the hallmarks of quantum condensed matter physics. One of their striking features is a bulk-boundary correspondence wherein the topological nature of the bulk manifests itself on boundaries via exotic…
We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the…
A Majorana fermion is the single fermionic particle that is its own antiparticle. Its dynamics is determined by the Majorana equation where the spinor field $(\psi)$ is by definition equal to its charge-conjugate field $(\psi_c)$. Here, we…
We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…
We investigate the transient effects occurring in a molecular quantum dot described by an Anderson-Holstein Hamiltonian which is instantly coupled to two fermionic leads biased by a finite voltage. In the limit of weak electron-phonon…
Two-component spinors are the basic ingredients for describing fermions in quantum field theory in four space-time dimensions. We develop and review the techniques of the two-component spinor formalism and provide a complete set of Feynman…
We consider the Jaynes-Cummings model of a single quantum spin $s$ coupled to a harmonic oscillator in a parameter regime where the underlying classical dynamics exhibits an unstable equilibrium point. This state of the model is relevant to…
We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving…
In a previous work [arXiv1905.01121] we have derived a quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical gravitational field. As standard matter is made of fermions, such…
Cooling methods and particle slowers as well as accelerators are basic tools for fundamental research and applications in different fields and systems. We put forward a generic mechanism to scale the momentum of a particle, regardless of…
We present simple classical dynamical models to address the question of introducing a stochastic nature in a time variable. These models include noise in the time variable but not in the "space" variable, which is opposite to the normal…
We analyze the quantum dynamics of the fractional-time Jaynes-Cummings model using a recent unitary framework for the fractional-time Schr\"odinger equation. We examine how the fractional derivative order $\alpha$ influences non-classical…
The mean-field approach to two-site Bose-Hubbard systems is well established and leads to nonlinear classical equations of motion for the population imbalance and the phase difference. It can, e.g., be based on the representation of the…