Related papers: Fractional Floquet theory

Fractional Floquet theory

URL: http://arxiv.org/abs/2302.02340v1
Date: Sun, 5 Feb 2023 09:01:32 GMT
Title: Fractional Floquet theory
Authors: Alexander Iomin
Abstract summary: The fractional Floquet theorem (fFT) is formulated in the form of the Mittag-Leffler function. The formula makes it possible to reduce the FTSE to the standard quantum mechanics with the time-dependent Hamiltonian.
Score: 91.3755431537592
License: http://creativecommons.org/licenses/by/4.0/
Abstract: A fractional generalization of the Floquet theorem is suggested for fractional Schr\"odinger equations (FTSE)s with the time-dependent periodic Hamiltonians. The obtained result, called the fractional Floquet theorem (fFT), is formulated in the form of the Mittag-Leffler function, which is considered as the eigenfunction of the Caputo fractional derivative. The suggested formula makes it possible to reduce the FTSE to the standard quantum mechanics with the time-dependent Hamiltonian, where the standard Floquet theorem is valid. Two examples related to quantum resonances are considered as well to support the obtained result.

Related papers

Continuous Floquet Theory in Solid-State NMR [0.0]
Continuous Floquet theory extends traditional Floquet theory to non-continuous Hamiltonians. We present closed-form expressions for computing first and second-order effective Hamiltonians. We show examples of the practical application of Continuous Floquet theory by investigating several solid-state NMR experiments.
arXiv Detail & Related papers (2024-04-09T13:27:33Z)
Simultaneous symmetry breaking in spontaneous Floquet states: Floquet-Nambu-Goldstone modes, Floquet thermodynamics, and the time operator [49.1574468325115]
We study simultaneous symmetry-breaking in a spontaneous Floquet state, focusing on the specific case of an atomic condensate. We first describe the quantization of the Nambu-Goldstone (NG) modes for a stationary state simultaneously breaking several symmetries of the Hamiltonian. We extend the formalism to Floquet states simultaneously breaking several symmetries, where Goldstone theorem translates into the emergence of Floquet-Nambu-Goldstone modes with zero quasi-energy.
arXiv Detail & Related papers (2024-02-16T16:06:08Z)
Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
arXiv Detail & Related papers (2023-02-27T18:56:40Z)
Stability of time-periodic $\mathcal{PT}$ and anti-$\mathcal{PT}$-symmetric Hamiltonians with different periodicities [0.0]
Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory. Time-periodicity offers avenues to engineer the landscape of Floquet quasi-energies across the complex plane.
arXiv Detail & Related papers (2023-01-16T04:30:06Z)
Real-Space, Real-Time Approach to Quantum-Electrodynamical Time-Dependent Density Functional Theory [55.41644538483948]
The equations are solved by time propagating the wave function on a tensor product of a Fock-space and real-space grid. Examples include the coupling strength and light frequency dependence of the energies, wave functions, optical absorption spectra, and Rabi splitting magnitudes in cavities.
arXiv Detail & Related papers (2022-09-01T18:49:51Z)
A continuous approach to Floquet theory for pulse-sequence optimization in solid-state NMR [0.0]
We present a framework that uses a continuous frequency space to describe and design solid-state NMR experiments. The approach is similar to the well established Floquet treatment for NMR, but is not restricted to periodic Hamiltonians.
arXiv Detail & Related papers (2022-07-12T13:26:44Z)
Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
arXiv Detail & Related papers (2022-05-24T20:51:03Z)
Defining a well-ordered Floquet basis by the average energy [0.0]
Floquet theory and the Floquet eigenbasis are used to compute the state of periodically driven quantum systems. We redefine the eigenbasis using a revised definition of the average energy as a quantum number. We obtain a Floquet-Ritz variational principle, and justify the truncation of the Hilbert space.
arXiv Detail & Related papers (2020-05-12T09:15:16Z)
Entanglement robustness to excitonic spin precession in a quantum dot [43.55994393060723]
A semiconductor quantum dot (QD) is an attractive resource to generate polarization-entangled photon pairs. We study the excitonic spin precession (flip-flop) in a family of QDs with different excitonic fine-structure splitting (FSS) Our results reveal that coherent processes leave the time post-selected entanglement of QDs unaffected while changing the eigenstates of the system.
arXiv Detail & Related papers (2020-01-31T13:50:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.