Related papers: Transfer operators and topological field theory
We propose a Fokker-Planck equation (FPE) theory to describe stochastic fluctuation and relaxation processes of lattice vibration at a wide range of conditions, including those beyond the phonon gas (PG) limit. Using the time-dependent,…
The formalism of Ursell operators provides a self-consistent integral equation for the one-particle reduced operator. In three dimensions this technique yields values of the shift in the Bose-Einstein condensation (BEC) transition…
We deal with the Sobolev space theory for the stochastic partial differential equation (SPDE) driven by Wiener processes $$ \partial_{t}^{\alpha}u=\left( \phi(\Delta) u +f(u) \right) + \partial_t^\beta \sum_{k=1}^\infty \int_0^t…
The scattering approach to quantum transport through a disordered quasi-one-dimensional conductor in the insulating regime is discussed in terms of its transfer matrix $\bbox{T}$. A model of $N$ one-dimensional wires which are coupled by…
Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when…
The spectrum of the evolution Operator associated with a nonlinear stochastic flow with additive noise is evaluated by diagonalization in a polynomial basis. The method works for arbitrary noise strength. In the weak noise limit we…
A new type of disorder-driven electronic percolation transition is found for two-dimensional electron gas (2DEG), based on a quantum cellular automaton model. This transition is shown to be accompanied with a metal-insulator transition, as…
We consider conditional McKean-Vlasov stochastic differential equations (SDEs), such as the ones arising in the large-system limit of mean field games and particle systems with mean field interactions when common noise is present. The…
We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of…
The dynamics of Dirac-Weyl spin-polarized wavepackets driven by periodic electric field is considered for the electrons in a mesoscopic quantum dot formed at the edge of two-dimensional HgTe/CdTe topological insulator with Dirac-Weyl…
We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a…
Langlands posed the question of whether a local functorial transfer map of stable tempered characters can be interpolated by the transpose of a linear operator between spaces of stable orbital integrals of test functions. These so-called…
We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…
We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…
In a companion paper we derived a unique time-reversal-invariant stochastic generalization of the Liouville equation and showed that it coincides with the evolution equation for the Husimi $Q$-function in a broad class of bosonic quantum…
It remains an open problem if there are universal scaling functions across a topological quantum phase transition (TPT) without an order parameter, but with extended Fermi surfaces (FS ). Here, we study a simple system of fermions hopping…
In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged…
Topological Weyl semimetals (TWSs) are exotic crystals possessing emergent relativistic Weyl fermions connected by unique surface Fermi-arcs (SFAs) in their electronic structures. To realize the TWS state, certain symmetry (such as the…
The original intent of the Koopman-von Neumann formalism was to put classical and quantum mechanics on the same footing by introducing an operator formalism into classical mechanics. Here we pursue their path the opposite way and examine…
One of the long-standing puzzles in string theory has been on the existence of a four-dimensional de Sitter and quasi de Sitter configurations, the latter being defined with a temporally varying dark energy, in E_8 x E_8 and SO(32)…