Multi-Directional Periodic Driving of a Two-Level System beyond Floquet Formalism
- URL: http://arxiv.org/abs/2511.03977v1
- Date: Thu, 06 Nov 2025 01:59:17 GMT
- Title: Multi-Directional Periodic Driving of a Two-Level System beyond Floquet Formalism
- Authors: Michael Warnock, David A. Hague, Vesna F. Mitrovic,
- Abstract summary: We introduce an exact expression for the response of a semi-classical two-level quantum system subject to arbitrary periodic driving.<n>We use the $star$-resolvent formalism with the path-sum theorem to determine the exact series solution to Schr"odinger's equation.
- Score: 1.1470070927586018
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In this manuscript, we introduce an exact expression for the response of a semi-classical two-level quantum system subject to arbitrary periodic driving. Determining the transition probabilities of a two-level system driven by an arbitrary periodic waveform necessitates numerical calculations through methods such as Floquet theory, requiring the truncation of an infinite matrix. However, such truncation can lead to a loss of significant interference information, hindering quantum sensors or introducing artifacts in quantum control. To alleviate this issue, we use the $\star$-resolvent formalism with the path-sum theorem to determine the exact series solution to Schr\"odinger's equation, therefore providing the exact transition probability. The resulting series solution is generated from a compact kernel expression containing all of the information of the periodic drive and then expanded in a non-harmonic Fourier series basis given by the divided difference of complex exponentials with coefficients corresponding to products of generalized Bessel functions. The present method provides an analytical formulation for quantum sensors and control applications.
Related papers
- A Theoretical Framework for an Efficient Normalizing Flow-Based Solution to the Electronic Schrodinger Equation [8.648660469053342]
A central problem in quantum mechanics involves solving the Electronic Schrodinger Equation for a molecule or material.<n>We propose a solution via an ansatz which is cheap to sample from, yet satisfies the requisite quantum mechanical properties.
arXiv Detail & Related papers (2024-05-28T15:42:15Z) - Exploring Multiscale Quantum Media: High-Precision Efficient Numerical
Solution of the Fractional Schr\"odinger equation, Eigenfunctions with
Physical Potentials, and Fractionally-Enhanced Quantum Tunneling [0.0]
This work includes an open source code for communities from quantum experimentalists to applied mathematicians to easily and efficiently explore the solutions of the fractional Schr"odinger equation.
arXiv Detail & Related papers (2024-03-12T01:03:42Z) - A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits [37.84307089310829]
Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit.
Despite their promise, the trainability of these algorithms is hindered by barren plateaus.
We present a general Lie algebra that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits.
arXiv Detail & Related papers (2023-09-17T18:14:10Z) - A Potential Based Quantization Procedure of the Damped Oscillator [0.0]
We formulate the quantization of the dissipative oscillator, which aids understanding of the above mentioned.
We arrive at such an irreversible quantum theory by which the quantum losses can be described.
arXiv Detail & Related papers (2022-04-06T15:17:03Z) - Decimation technique for open quantum systems: a case study with
driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics.
We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function.
We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z) - Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables.
In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
arXiv Detail & Related papers (2021-02-18T20:55:04Z) - Dynamical formulation of low-energy scattering in one dimension [0.0]
A transfer matrix $mathbfM$ of a short-range potential may be expressed in terms of the time-evolution operator for an effective two-level quantum system.
We explore the utility of this formulation in the study of the low-energy behavior of the scattering data.
arXiv Detail & Related papers (2021-02-11T15:55:34Z) - Evolution of a Non-Hermitian Quantum Single-Molecule Junction at
Constant Temperature [62.997667081978825]
We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments.
We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
arXiv Detail & Related papers (2021-01-21T14:33:34Z) - The role of boundary conditions in quantum computations of scattering
observables [58.720142291102135]
Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution.
As with present-day calculations, quantum computation strategies still require the restriction to a finite system size.
We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
arXiv Detail & Related papers (2020-07-01T17:43:11Z) - Quantum Statistical Complexity Measure as a Signalling of Correlation
Transitions [55.41644538483948]
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions.
We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain.
We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
arXiv Detail & Related papers (2020-02-05T00:45:21Z) - Discrete Adjoints for Accurate Numerical Optimization with Application
to Quantum Control [0.0]
This paper considers the optimal control problem for realizing logical gates in a closed quantum system.
The system is discretized with the Stormer-Verlet scheme, which is a symplectic partitioned Runge-Kutta method.
A parameterization of the control functions based on B-splines with built-in carrier waves is also introduced.
arXiv Detail & Related papers (2020-01-04T00:02:23Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.