Related papers: A Closed-Form Approach to Oscillatory Integrals in…
The Landau collision integral is often considered the gold standard in the context of kinetic plasma simulation due to its conservative properties, despite challenges involved in its discretization. The primary challenge when implementing…
We determine transition probabilities in two exactly solvable multistate Landau-Zener (LZ) models and discuss applications of our results to the theory of dynamic passage through a phase transition in the dissipationless quantum mechanical…
We propose new semi-implicit numerical methods for the integration of the stochastic Landau-Lifshitz equation with built-in angular momentum conservation. The performance of the proposed integrators is tested on the 1D Heisenberg chain. For…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
Landau levels in certain models are known to protrude into the zero-field energy gap. These are known as anomalous Landau levels (ALLs). We study whether ALLs can lead to Fermi-surface like quantum oscillation in the absence of a zero-field…
The efficient approximation of highly oscillatory integrals plays an important role in a wide range of applications. Whilst traditional quadrature becomes prohibitively expensive in the high-frequency regime, Levin methods provide a way to…
We consider the interaction-round-a-face version of the six-vertex model for arbitrary anisotropy parameter, which allow us to derive an integrable one-dimensional quantum Hamiltonian with three-spin interactions. We apply the quantum…
In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and…
We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an appropriate sense and behave well under perturbations of the…
We discuss the strong interaction regime of the nonlinear Landau-Zener problem coming up at coherent photo- and magneto-association of ultracold atoms. We apply a variational approach to an exact third-order nonlinear differential equation…
Interfaces between lamellar and disordered phases, and grain boundaries within lamellar phases, are investigated employing a simple Landau free energy functional. The former are examined using analytic, approximate methods in the weak…
The Landauer formula allows us to describe theoretically the conductance in terms of the transmission function in a mesoscopic system. We propose a general method to evaluate the transmission function in the complex domain for systems…
For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but…
We present a general protocol to control closed quantum systems that is based on minimising the adiabatic action. Using tools based on the geometry of quantum evolutions through the quantum adiabatic brachistochrone, we show that high…
The Kraus representation of quantum channels allows for a precise emulation of the complex dynamics that take place on quantum processors, whether for benchmarking algorithms, predicting the performance of error correction and mitigation,…
We investigate the dielectric breakdown of mesoscopic Mott insulators, a phenomenon where a strong electric field destabilizes the insulating state, resulting in a transition to a metallic phase. Using the Landau-Zener formalism, which…
Steepest descent methods combining complex contour deformation with numerical quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory integrals. However, unless the phase function governing the…