A non-perturbative analysis of spin-boson interactions using the Weyl relations

A novel approach to perturbative calculations for a large class of interacting boson theories

We present a method of calculating the interacting S-matrix to an arbitrary perturbative order for a large class of boson interaction Lagrangians. The method takes advantage of a previously unexplored link between the $n$-point Green's function and a certain system of linear Diophantine equations. By finding all nonnegative solutions of the system, the task of perturbatively expanding an interacting $S$-matrix becomes elementary for any number of interacting fields, to an arbitrary perturbative order (irrespective of whether it makes physical sense) and for a large class of scalar boson theori…

Maslov's complex germ and the Weyl--Moyal algebra in quantum mechanics and in quantum field theory

The paper is a survey of some author's results related with the Maslov--Shvedov method of complex germ and with quantum field theory. The main idea is that many results of the method of complex germ and of perturbative quantum field theory can be made more simple and natural if instead of the algebra of (pseudo)differential operators one uses the Weyl algebra (operators with Weyl symbols) with the Moyal *-product. Section 1, devoted to quantum mechanics, contains a closed mathematical description of the Maslov--Shvedov method in the theory of Schrodinger equation, including the method of canon…

Heat transfer in a nonequilibrium spin-boson model: A perturbative approach

We investigate the heat transport in a nonequilibrium spin-boson model, where a two level system bridging two harmonic reservoirs at different temperatures, by employing a unitary transformation along with a resolvent operator expansion technique. Analytical expressions of the heat current and the thermal conductance of this model are obtained. Compared with the performances of other methods, namely, the nonequilibrium Green's function method and the equation of motion formulation, our approach provides a reasonable description of heat transfer properties of the nonequilibrium spin-boson model…

Pseudomode description of general open quantum system dynamics: non-perturbative master equation for the spin-boson model

We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment defined by a generalized spectral density function. The method is based on replacing the environment by a set of damped harmonic oscillators - the pseudomodes - thereby forming an enlarged open system whose dynamics is governed by a Markovian master equation. Each pseudomode is connected to one of the poles of the spectral density when analytically continued to the lower-half complex frequency plane. Here, we extend previous results to a completely generic class of …

Quantum annealing in spin-boson model: from a perturbative to a ultrastrong mediated coupling

We study a quantum annealer where bosons mediate the Ising-type interactions between qubits. We compare the efficiency of ground state preparation for direct and mediated couplings, for which Ising and spin-boson Hamiltonian are employed respectively. This comparison is done numerically for a small frustrated antiferromagnet, with a careful choice of the optimal adiabatic passage that reveals the features of the boson-mediated interactions. Those features can be explained by taking into account what we called excited solutions: states with the same spin correlations as the ground-state but wit…

高斯玻色环境中开放系统多时刻期望值的非微扰处理

Non-perturbative treatment of open-system multi-time expectation values in Gaussian bosonic environments

本文证明了开放量子系统在连续高斯玻色环境与由GKLS生成元演化的离散环境下多时刻期望值等价的条件，并提出用有限阻尼模式进行非微扰计算的方法。