相关论文: Quantum Gross Laplacian and Applications
In this note, we study the celebrated virial theorem for dissipative systems, both classical and quantum. The classical formulation is discussed and an intriguing effect of the random force (noise) is made explicit in the context of the…
The quantum states representing classical phase space are given, and these are used to formulate quantum statistical mechanics as a formally exact double perturbation expansion about classical statistical mechanics. One series of quantum…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
As a first step at developing a theory of noncommutative nonlinear elliptic partial differential equations, we analyze noncommutative analogues of Laplace's equation and its variants (some of the them nonlinear) over noncommutative tori.…
Working towards an algebra for operators of strongly interacting quantum fields, a nonassociative decomposition of field operators is proposed. In the demonstrated case, quantum corrections appear from the possible bracket permutations. A…
In this paper, we define a Laplacian operator on a statistical manifold, called the vector Laplacian. This vector Laplacian incorporates information from the Amari-Chentsov tensor. We derive a formula for the vector Laplacian. We also give…
We show that a semi-commutative Galois extension of a unital associative algebra can be endowed with the structure of a graded q-differential algebra. We study the first and higher order noncommutative differential calculus of…
We apply the linear delta expansion to the quantum mechanical version of the slow rollover transition which is an important feature of inflationary models of the early universe. The method, which goes beyond the Gaussian approximation,…
In order to solve quantum field theory in a non-perturbative way, Lagrangian lattice simulations have been very successful. Here we discuss a recently proposed alternative Hamiltonian lattice formulation - the Monte Carlo Hamiltonian. In…
In this note we introduce some nonlinear extremal nonlocal operators that approximate the, so called, truncated Laplacians. For these operators we construct representation formulas that lead to the construction of what, with an abuse of…
We study second-order elliptic partial differential operators acting on sections of vector bundles over a compact manifold with boundary with a non-scalar positive definite leading symbol. Such operators, called non-Laplace type operators,…
We investigate the dynamics of a quantum system coupled linearly to Gaussian white noise using functional methods. By performing the integration over the noisy field in the evolution operator, we get an equivalent non-Hermitian Hamiltonian,…
We propose a Langevin equation to describe the quantum Brownian motion of bounded particles based on a distinctive formulation concerning both the fluctuation and dissipation forces. The fluctuation force is similar to that employed in the…
Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymptotic expressions for the points and weights of Gaussian…
This paper presents a quantum field theoretical formalism for studying magnons in finite nanostructures with arbitrary shapes and spatially nonuniform ground states. It extends the classical micromagnetic formalism by introducing a…
We formulate the lattice QCD simulation with background classical gravitational fields. This formulation enables us to study nonperturbative aspects of quantum phenomena in curved spacetimes from the first principles. As the first…
The relativistic quantum equation is proposed for the complex wave function, which has the meaning of a probability amplitude. The Lagrangian formulation of the proposed theory is developed. The problem of spreading of a wave packet in an…
Gaussian quantum channels are well understood and have many applications, e.g., in Quantum Information Theory and in Quantum Optics. For more general quantum channels one can in general use semiclassical approximations or perturbation…
We offer an alternative to the conventional network formulation of quantum computing. We advance the analog approach to quantum logic gate/circuit construction. As an illustration, we consider the spatially extended NOT gate as the first…
The fractional Laplacian $(-\Delta)^{\alpha/2}$ is a non-local operator which depends on the parameter $\alpha$ and recovers the usual Laplacian as $\alpha \to 2$. A numerical method for the fractional Laplacian is proposed, based on the…