Related papers: Exact Quantum Trace Formula from Complex Periodic Orbits

Exact Quantum Trace Formula from Complex Periodic Orbits

URL: http://arxiv.org/abs/2411.10691v1
Date: Sat, 16 Nov 2024 03:58:24 GMT
Title: Exact Quantum Trace Formula from Complex Periodic Orbits
Authors: Chaoming Song,
Abstract summary: We explore the full quantum version of the trace formula using the Lefschetz thimble method. Our key innovation lies in the simultaneous complexification of the periods of cycles, resulting in a fully quantum trace formula. This formulation connects the quantum spectrum to contributions across all complex time directions, encompassing all relevant homology classes.
Score: 0.4506616924250028
License:
Abstract: The Gutzwiller trace formula establishes a profound connection between the quantum spectrum and classical periodic orbits. However, its application is limited by its reliance on the semiclassical saddle point approximation. In this work, we explore the full quantum version of the trace formula using the Lefschetz thimble method by incorporating complexified periodic orbits. Upon complexification, classical real periodic orbits are transformed into cycles on compact Riemann surfaces. Our key innovation lies in the simultaneous complexification of the periods of cycles, resulting in a fully quantum trace formula that accounts for all contributions classified by the homology classes of the associated Riemann surfaces. This formulation connects the quantum spectrum to contributions across all complex time directions, encompassing all relevant homology classes. Our approach naturally unifies and extends two established methodologies: periodic orbits in real time, as in Gutzwiller's original work, and quantum tunneling in imaginary time, as in the instanton method.

Related papers

Order-chaos transition in correlation diagrams and quantization of period orbits [0.0]
We show how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.
arXiv Detail & Related papers (2024-01-25T19:02:15Z)
Energy transition density of driven chaotic systems: A compound trace formula [0.0]
Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian have been shown to depend on closed compound orbits. The phase of the oscillations with the energies or evolution parameters agree with those previously obtained. The amplitude of the contribution of each closed compound orbit is more compact and independent of any feature of the Weyl-Wigner representation.
arXiv Detail & Related papers (2022-10-08T18:10:12Z)
Complex time method for quantum dynamics when an exceptional point is encircled in the parameter space [0.0]
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.
arXiv Detail & Related papers (2021-10-27T14:41:44Z)
Wave Functional of the Universe and Time [62.997667081978825]
A version of the quantum theory of gravity based on the concept of the wave functional of the universe is proposed. The history of the evolution of the universe is described in terms of coordinate time together with arbitrary lapse and shift functions.
arXiv Detail & Related papers (2021-10-18T09:41:59Z)
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)
Periodic orbit evaluation of a spectral statistic of quantum graphs without the semiclassical limit [0.0]
We evaluate a spectral statistic of chaotic 4-regular quantum graphs from their periodic orbits without the semiclassical limit. We observe the mechanism that connects semiclassical results to the total number of orbits regardless of their structure.
arXiv Detail & Related papers (2020-12-29T22:57:30Z)
Quantum particle across Grushin singularity [77.34726150561087]
We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
arXiv Detail & Related papers (2020-11-27T12:53:23Z)
Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit [58.720142291102135]
Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties. We experimentally study a synthetic quantum Hall effect with a two-tone drive.
arXiv Detail & Related papers (2020-04-07T15:00:41Z)
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.