Complex time method for quantum dynamics when an exceptional point is encircled in the parameter space

• URL: http://arxiv.org/abs/2110.14473v2
• Date: Tue, 11 Jan 2022 10:35:07 GMT
• Title: Complex time method for quantum dynamics when an exceptional point is encircled in the parameter space
• Authors: Petra Ruth Kapralova-Zdanska
• Abstract summary: We revisit the complex time method for the application to quantum dynamics as an exceptional point is encircled in the parameter space of the Hamiltonian. We discuss a switch between Rabi oscillations and rapid adiabatic passage which occurs upon the encircling of an exceptional point in a special time-symmetric case.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We revisit the complex time method for the application to quantum dynamics as an exceptional point is encircled in the parameter space of the Hamiltonian. The basic idea of the complex time method is using complex contour integration to perform the first-order adiabatic perturbation integral. In this way, the quantum dynamical problem is transformed to a study of singularities in the complex time plane -- transition points -- which represent complex degeneracies of the adiabatic Hamiltonian as the time-dependent parameters defining the encircling contour are analytically continued to complex plane. As an underlying illustration of the approach we discuss a switch between Rabi oscillations and rapid adiabatic passage which occurs upon the encircling of an exceptional point in a special time-symmetric case.

Related papers

• Quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis [0.0]
  We revisit the path integral description of quantum tunneling and show how it can be generalized to excited states. For clarity, we focus on the simple toy model of a point particle in a double-well potential, for which we perform all steps explicitly. We find that, for systems without an explicit time-dependence, our approach reproduces the picture of an instanton-like solution defined on a finite Euclidean-time interval.
  arXiv  Detail & Related papers  (2024-01-31T19:00:00Z)
• A magnetic clock for a harmonic oscillator [89.99666725996975]
  We study how the quantum dynamics transforms into a classical-like behaviour when conditions related with macroscopicity are met by the clock alone. In the description of this emerging behaviour finds its place the classical notion of time, as well as that of phase-space and trajectories on it.
  arXiv  Detail & Related papers  (2023-10-20T09:55:51Z)
• Complex classical paths in quantum reflections and tunneling [0.0]
  We explain how the interference pattern in the real-time propagator and energy propagator is organized by caustics and Stoke's phenomena. We demonstrate how singularity crossings play a central role in the real-time description of quantum tunneling.
  arXiv  Detail & Related papers  (2023-09-21T18:43:24Z)
• Unraveling the bounce: a real time perspective on tunneling [0.0]
  We study tunneling in one-dimensional quantum mechanics using the path integral in real time, where solutions of the classical equation of motion live in the complex plane. We show explicitly how the imaginary time bounce arises as a parameterization of the lowest order term in the energy expansion.
  arXiv  Detail & Related papers  (2023-09-14T10:35:39Z)
• Indication of critical scaling in time during the relaxation of an open quantum system [34.82692226532414]
  Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found.
  arXiv  Detail & Related papers  (2022-08-10T05:59:14Z)
• Spatio-Temporal Variational Gaussian Processes [26.60276485130467]
  We introduce a scalable approach to Gaussian process inference that combinestemporal-temporal filtering with natural variational inference. We derive a sparse approximation that constructs a state-space model over a reduced set of inducing points. We show that for separable Markov kernels the full sparse cases recover exactly the standard variational GP.
  arXiv  Detail & Related papers  (2021-11-02T16:53:31Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them [0.0]
  We observe that the physics of a quantum system is intimately connected to the position of complex-valued energy singularities. We highlight work on the convergence behaviour of perturbative series obtained within Moller--Plesset perturbation theory.
  arXiv  Detail & Related papers  (2020-12-07T13:42:40Z)
• Complexity and Floquet dynamics: non-equilibrium Ising phase transitions [0.0]
  We study the time-dependent circuit complexity of the periodically driven transverse field Ising model. In the high-frequency driving limit the system is known to exhibit non-equilibrium phase transitions governed by the amplitude of the driving field.
  arXiv  Detail & Related papers  (2020-08-31T19:13:03Z)
• From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics [68.8204255655161]
  We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process. We show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear dynamics.
  arXiv  Detail & Related papers  (2020-01-13T14:30:36Z)

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.