Related papers: Jaynes-Cummings model without rotating wave approx…
Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which evoked an explosion of applications with the blooming of atomic and subatomic physics. Even though PT is well-used today,…
The non-Hermitian but $\mathcal{PT}$-symmetric quantum field theories are known to have a pseudo-Hermitian interpretation. However the corresponding intertwining operator happens to be nonlocal that raises the question to what extent this…
In this work, we examine spectral properties of Markov transition operators corresponding to Gaussian perturbations of discrete time dynamical systems on the circle. We develop a method for calculating asymptotic expressions for eigenvalues…
We study estimation in the linear model $y=A\beta^\star+\epsilon$, in a Bayesian setting where $\beta^\star$ has an entrywise i.i.d. prior and the design $A$ is rotationally-invariant in law. In the large system limit as dimension and…
This article presents a general master equation formalism for the interaction between travelling pulses of quantum radiation and localized quantum systems. Traveling fields populate a continuum of free space radiation modes and the…
Quantum mechanics of unitary systems is considered in quasi-Hermitian representation. In this framework the concept of perturbation is found counterintuitive, for three reasons. The first one is that in this formalism we are allowed to…
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…
We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…
The system of equations for parametric sub-resonant growth of the amplitude of oscillations was obtained. The time of turning point from the growing of the amplitude to the bounded oscillations in the slow variable was found. The comparison…
A new two-step renormalization procedure is proposed. In the first step, the effects of high-energy states are considered in the conventional (Feynman) perturbation theory. In the second step, the coupling to many-body states is eliminated…
We consider a quasi-linear Hamiltonian system with one and a half degrees of freedom. The Hamiltonian of this system differs by a small, $\sim\varepsilon$, perturbing term from the Hamiltonian of a linear oscillatory system. We consider…
A perturbation decaying to 0 at infinity and not too irregular at 0 introduces at most a discrete set of eigenvalues into the spectral gaps of a one-dimensional Dirac operator on the half-line. We show that the number of these eigenvalues…
We construct a perturbation theory which we conjecture to be free of the Coulomb-phase infrared divergence. This perturbation theory is developed for one of the simplest yet prototypical scattering amplitudes which would otherwise exhibit…
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle non-relativisitic confining potential model. In this model asymptotic freedom follows from the similarity of the free-particle and bound state radial…
In this article we focus on estimating the quadratic covariation of continuous semimartingales from discrete observations that take place at asynchronous observation times. The Hayashi-Yoshida estimator serves as synchronized realized…
We analyze in detail an open cavity array using mean-field description, where each cavity field is coupled to a number of three-level atoms. Such system is highly tunable and can be described by a Jaynes-Cummings like Hamiltonian with…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We highlight the importance of quantum fluctuations in organizing a dissipative quantum phase transition for the driven Jaynes-Cummings interaction with variable qubit-cavity detuning. The system response presents a substantial difference…
Within quantum mechanics model we study the problem of resummation of an asymptotic perturbation series for bound state parameters via optimization of the perturbative expansion. A possible application of the method to the positronium…
Using the theory of self-adjoint extensions, we construct all the possible hamiltonians describing the non relativistic Aharonov-Bohm effect. In general the resulting hamiltonians are not rotationally invariant so that the angular momentum…