Related papers: Stochastic Path Integral Formulation of Full Count…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of non-linear control problems that can be formulated as a path integral and where the noise plays the role of…
We implement in systems of fermions the formalism of pseudoclassical paths that we recently developed for systems of bosons and show that quantum states of fermionic fields can be described, in the Heisenberg picture, as linear combinations…
A path integral method, combined with atomistic spin dynamics simulations, has been developed to calculate thermal quantum expectation values using a classical approach. In this study, we show how to treat Hamiltonians with non-linear…
A theory of electron counting statistics in quantum transport is presented. It involves an idealized scheme of current measurement using a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current. Within…
We consider the continuity equation for open chaotic quantum systems in the semiclassical limit. First we explicitly calculate a semiclassical expansion for the probability current density using an expression based on classical…
We investigate the influence of spin-orbit interaction on ballistic transport through chaotic cavities by using semiclassical methods. Our approach is based on the Landauer formalism and the Fisher-Lee relations, appropriately generalized…
Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is…
We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…
Full counting statistics is a fundamentally new concept in quantum transport. After a review of basic statistics theory, we introduce the powerful Green's function approach to full counting statistics. To illustrate the concept we consider…
We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for…
We consider the zero frequency fluctuations of charge inside a mesoscopic conductor in the large capacitance limit. In analogy to current counting statistics we derive the characteristic function of charge fluctuations in terms of the…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
The semiclassical approximation of the worldline path integral is a powerful tool to study nonperturbative electron-positron pair creation in spacetime-dependent background fields. Finding solutions of the classical equations of motion,…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White…
We present the systematic formalism to derive the path-integral formulation for the hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and…
We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths…
Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path…
The behavior of the most probable values of the order parameter $x$ and the amplitude $\phi$ of conjugate force fluctuations is studied for a stochastic system with a colored multiplicative noise with absorbing states. The phase diagrams…