Quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis

• URL: http://arxiv.org/abs/2402.00099v1
• Date: Wed, 31 Jan 2024 19:00:00 GMT
• Title: Quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis
• Authors: Thomas Steingasser, David I. Kaiser
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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. Instead of performing the familiar Wick rotation from physical to imaginary time - which is inconsistent with the requisite boundary conditions when treating tunneling from excited states - we regularize the path integral by adding an infinitesimal complex contribution to the Hamiltonian, while keeping time strictly real. We find that this gives rise to a complex stationary-phase solution, in agreement with recent insights from Picard-Lefshitz theory. We then show that there exists a class of analytic solutions for the corresponding equations of motion, which can be made to match the appropriate boundary conditions in the physically relevant limits of a vanishing regulator and an infinite physical time. We provide a detailed discussion of this non-trivial limit. 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. Lastly, we discuss the generalization of our approach to broader classes of systems, for which it serves as a reliable framework for high-precision calculations.

Related papers

• Proof of a Universal Speed Limit on Fast Scrambling in Quantum Systems [0.0]
  We prove that the time required for sustained information scrambling in any Hamiltonian quantum system is universally at least logarithmic in the entanglement entropy of scrambled states. This addresses two foundational problems in nonequilibrium quantum dynamics.
  arXiv  Detail & Related papers  (2024-04-23T18:00:01Z)
• A Realist Interpretation of Unitarity in Quantum Gravity [0.0]
  Unitarity is a difficult concept to implement in canonical quantum gravity because of state non-normalizability and the problem of time. We use the postulate of a definite configuration in the theory to define a global time for the gravitational-fermionic system. We find unitary states in mini-superspace by finding an approximate solution to the Hamiltonian constraint.
  arXiv  Detail & Related papers  (2023-10-23T17:56:28Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• 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)
• Measurement events relative to temporal quantum reference frames [44.99833362998488]
  We compare two consistent approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements. We show that for non-ideal clocks, the purified measurement approach yields time non-local, non-unitary evolution.
  arXiv  Detail & Related papers  (2023-08-21T18:26:12Z)
• Exact universal bounds on quantum dynamics and fast scrambling [0.0]
  We show that the spectral form factor sets a universal state-independent bound on the quantum dynamics of a complete set of initial states over arbitrarily long times. We use this result to constrain the scrambling of information in interacting many-body systems.
  arXiv  Detail & Related papers  (2022-12-28T18:47:20Z)
• A shortcut to adiabaticity in a cavity with a moving mirror [58.720142291102135]
  We describe for the first time how to implement shortcuts to adiabaticity in quantum field theory. The shortcuts take place whenever there is no dynamical Casimir effect. We obtain a fundamental limit for the efficiency of an Otto cycle with the quantum field as a working system.
  arXiv  Detail & Related papers  (2022-02-01T20:40:57Z)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• 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)
• 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)
• Time-optimal quantum transformations with bounded bandwidth [0.0]
  We derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state. In a final section, we use the quantum speed limits to obtain upper bounds on the power with which energy can be extracted from quantum batteries.
  arXiv  Detail & Related papers  (2020-11-24T08:42:08Z)

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.