Related papers: Generalised fractional Rabi problem
We deliver a novel approach towards the variational description of Lagrangian mechanical systems subject to fractional damping by establishing a restricted Hamilton's principle. Fractional damping is a particular instance of non-local (in…
This letter extends previous findings on the modified Schr\"odinger evolution inspired by quantum gravity phenomenology. By establishing a connection between this approach and fractional quantum mechanics, we provide insights into a…
We establish a simple quantitative relationship between the environmental memory effects and the characteristics in a dynamical decoupling process. In contrast to previous works, our measures of non-Markovianity are tailored and extended to…
This paper is focused on local and global stability of a fractional-order predator-prey model with habitat complexity constructed in the Caputo sense and corresponding discrete fractional-order system. Mathematical results like positivity…
We investigate memory effects and quantum transport in two-dimensional lattice systems within the framework of non-equilibrium Green's functions and Schwinger-Keldysh non-equilibrium quantum field theory. Starting from a 2D tight-binding…
The physics of quantum states beyond thermodynamic equilibrium represents a fascinating and cutting-edge research. Using numerical state-of-the-art approaches, we observe dynamical quantum phase transitions in the dissipative two-qubit Rabi…
The exact quantum dynamics of a single spin-1/2 in a generic time-dependent classical magnetic field is investigated and compared with the quantum motion of a spin-1/2 studied by Rabi and Schwinger. The possibility of regarding the scenario…
The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are…
We study the dynamical properties of the quantum Rabi model within a systematic expansion method. Based on the observation that the parity symmetry of the Rabi model is kept during the evolution of the states, we decompose the initial state…
Periodically driven quantum systems host exotic phenomena which often do not have any analog in undriven systems. Floquet prethermalization and dynamical freezing of certain observables, via the emergence of conservation laws, are realized…
We develop a theory of the Cauchy problem for linear evolution systems of partial differential equations with the Caputo-Dzrbashyan fractional derivative in the time variable $t$. The class of systems considered in the paper is a fractional…
Derivatives of fractional order with respect to time describe long-term memory effects. Using nonlinear differential equation with Caputo fractional derivative of arbitrary order $\alpha>0$, we obtain discrete maps with power-law memory.…
We present a theoretical study of the spin dynamics of a single electron confined in a quantum dot. Spin dynamics is induced by the interplay of electrical driving and the presence of a spatially disordered magnetic field, the latter being…
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size $n$. We use as an example the…
Coherent errors constitute a significant barrier to successful large-scale quantum computation. One such error mechanism is crosstalk, which violates spatial locality or the independence of operations. We present a description of crosstalk…
We explore the coherent transfer of electronic signatures from a strongly correlated, optically gated nanoscale quantum dot to a weakly interacting, electrically backgated microscale channel. In this unique side-coupled `T' geometry for…
Driven quantum systems subject to non-Markovian noise are typically difficult to model even if the noise is classical. We present a systematic method based on generalized cumulant expansions for deriving a time-local master equation for…
Periodic driving plays a central role in quantum control, but its application in interacting spin systems is often restricted to near-resonant conditions, where standard averaging techniques remain valid. Here we investigate how detuning…
In this paper we discuss both analytically and numerically the rich quantum dynamics of the spin-boson model driven by a time-independent field of photon. Interestingly, we predict a new Rabi oscillation, whose period is inversely…
We develop the theory of fractional gradient flows: an evolution aimed at the minimization of a convex, l.s.c.~energy, with memory effects. This memory is characterized by the fact that the negative of the (sub)gradient of the energy equals…