Related papers: Unifying semiclassics and quantum perturbation the…
Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to the…
We introduce the theory of non-linear cosmological perturbations using the correspondence limit of the Schr\"odinger equation. The resulting formalism is equivalent to using the collisionless Boltzman (or Vlasov) equations which remain…
The three-wave resonant interaction equations are a non-dispersive system of partial differential equations with quadratic coupling describing the time evolution of the complex amplitudes of three resonant wave modes. Collisions of wave…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…
We study the second-order optical response of Weyl semimetals in the presence of a magnetic field. We consider an idealized model of a perfectly linear Weyl node and use the Kubo formula at zero temperature to calculate the intrinsic…
The nonlinear Hall effect has attracted considerable attention and undergone extensive investigation in recent years. However, theoretical studies addressing size-dependent effects remain largely unexplored. In this work, we establish a…
We demonstrate that the non-Hermitian quantum geometric tensor (QGT) governs nonlinear electrical responses in systems with a spectral line gap. The quantum metric, which is the symmetric component of the QGT and takes complex values in…
In recent years, there has been growing interest in non-Hermitian phenomena in low-symmetry conductors, particularly optical gain driven by electro-optic effects. Conventional semiclassical treatments typically attribute these effects to…
Starting from a general $N$-band Hamiltonian with weak spatial and temporal variations, we derive a low energy effective theory for transport within one or several overlapping bands. To this end, we use the Wigner representation that allows…
We consider the inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open…
The semi-classical Bloch-Boltzmann theory is at the heart of our understanding of conduction in solids, ranging from metals to semi-conductors. Physical systems that are beyond the range of applicability of this theory are thus of…
The Boltzmann-Langevin equation is used to relate the shot-noise power of a mesoscopic conductor to classical transmission probabilities at the Fermi level. This semiclassical theory is applied to tunneling through n barriers in series. For…
This paper examines the properties of the self-energy operator in lattice-matched semiconductor heterostructures, focusing on nonanalytic behavior at small values of the crystal momentum, which gives rise to long-range Coulomb potentials. A…
Excitonic effects in the linear optical response of semiconductors are well-known and the subject of countless experimental and theoretical studies. For the technologically important second order nonlinear response, however, description of…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by…
This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…
We study conformal quantum mechanics by first considering the perturbative $S$-matrix in various dimensions. The model has two couplings and we study perturbatively the degree of ultraviolet divergences arising in the interplay between the…
We explore the charge transport mechanism in organic semiconductors based on a model that accounts for the thermal intermolecular disorder at work in pure crystalline compounds, as well as extrinsic sources of disorder that are present in…