Dynamical invariant formalism of shortcuts to adiabaticity

• URL: http://arxiv.org/abs/2209.04367v1
• Date: Fri, 9 Sep 2022 15:59:39 GMT
• Title: Dynamical invariant formalism of shortcuts to adiabaticity
• Authors: Kazutaka Takahashi
• Abstract summary: We discuss how the method allows us to realize adiabatic dynamics. We introduce examples of Lax pair, quantum brachistochrone, and flow equation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We give a pedagogical introduction to dynamical invariant formalism of shortcuts to adiabaticity. For a given operator form of the Hamiltonian with undetermined coefficients, the dynamical invariant is introduced to design the coefficients. We discuss how the method allows us to realize adiabatic dynamics and describe a relation to the counterdiabatic formalism. The equation for the dynamical invariant takes a familiar form and is often used in various fields of physics. We introduce examples of Lax pair, quantum brachistochrone, and flow equation.

Related papers

• Quantum entanglement as an ambiguity of classical dynamics [1.534667887016089]
  We study consequences of applying formalism of symplectic geometry to quantum mechanics. We show that this degeneracy can be understood as an ambiguity of some classical dynamic.
  arXiv  Detail & Related papers  (2024-10-29T11:07:48Z)
• Dual symplectic classical circuits: An exactly solvable model of many-body chaos [0.0]
  We prove that two-point dynamical correlation functions are non-vanishing only along the edges of the light cones. We test our theory in a specific family of dual-symplectic circuits, describing the dynamics of a classical Floquet spin chain.
  arXiv  Detail & Related papers  (2023-07-04T15:48:41Z)
• Hybrid completely positive Markovian quantum-classical dynamics [0.0]
  derivation of hybrid quantum-classical dynamics is given in terms of Markovian master equations. Goal is a brief introduction to state-of-the-art of hybrid dynamics.
  arXiv  Detail & Related papers  (2023-02-26T22:10:38Z)
• Lindblad master equations for quantum systems coupled to dissipative bosonic modes [0.0]
  We derive Lindblad master equations for a subsystem whose dynamics is coupled to bosonic modes. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins. This master equation accurately predicts the Dicke phase transition and gives the correct steady state.
  arXiv  Detail & Related papers  (2022-03-07T11:21:48Z)
• 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)
• 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)
• Nonlinear Description of Quantum Dynamics. Generalized Coherent States [0.0]
  In this work it is shown that there is an inherent nonlinear evolution in the dynamics of the so-called generalized coherent states. The immersion of a classical manifold into the Hilbert space of quantum mechanics is employed.
  arXiv  Detail & Related papers  (2020-09-07T16:47:51Z)
• Abstract Dynamical Systems: Remarks on Symmetries and Reduction [77.34726150561087]
  We show how an algebraic formulation for the dynamics of a physical system allows to describe a reduction procedure for both classical and quantum evolutions. We conclude by showing how this formulation allows to describe a reduction procedure for both classical and quantum evolutions.
  arXiv  Detail & Related papers  (2020-08-26T17:32:38Z)
• Dissipative flow equations [62.997667081978825]
  We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
  arXiv  Detail & Related papers  (2020-07-23T14:47:17Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems [74.80320120264459]
  We present an approach to learn such motions from a limited number of human demonstrations. The complex motions are encoded as rollouts of a stable dynamical system. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.
  arXiv  Detail & Related papers  (2020-05-27T03:51:57Z)

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.