The tunneling splitting and the Kramers theory of activated processes

• URL: http://arxiv.org/abs/2110.14445v1
• Date: Wed, 27 Oct 2021 14:02:07 GMT
• Title: The tunneling splitting and the Kramers theory of activated processes
• Authors: Pierpaolo Pravatto, Barbara Fresch, Giorgio J. Moro
• Abstract summary: The isomorphism between the Fokker-Planck-Smoluchowski operator and the Born-Oppenheimer quantum Hamiltonian is the key element of this method. The comparison with exact values of the tunneling splittings shows a much better accuracy than WKB semiclassical estimates.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The study of tunneling splitting is fundamental to get insight into the dynamics of a multitude of molecular systems. In this paper, a novel approach to the analysis of the ground-state tunneling splitting is presented and explicitly applied to one-dimensional systems. The isomorphism between the Fokker-Planck-Smoluchowski operator and the Born-Oppenheimer quantum Hamiltonian is the key element of this method. The localization function approach, used in the field of stochastic processes to study the Kramers problem, leads to a simple, yet asymptotically justified, integral approximation for the tunneling splitting. The comparison with exact values of the tunneling splittings shows a much better accuracy than WKB semiclassical estimates.

Related papers

• Benchmarking Proton Tunneling Splittings with a Wavefunction-Based Double-Well Model: Application to the Formic Acid Dimer [0.0]
  Proton tunneling across hydrogen bonds is a fundamental quantum effect with implications for spectroscopy, stability and biomolecular stability.<n>Here we develop a wavefunction-based framework for tunneling splittings using a Cornell-type double-well potential and apply it as a benchmark for hydrogen-bond tunneling.
  arXiv  Detail & Related papers  (2025-10-31T05:45:15Z)
• Ring-polymer instanton theory for tunneling between asymmetric wells [0.0]
  We develop a new formulation of instanton theory based on a projected flux correlation function.<n>The theory is then applied to study tunneling between non-degenerate minima in the biomolecule $alpha$-fenchol.
  arXiv  Detail & Related papers  (2025-10-30T15:18:03Z)
• Zassenhaus Expansion in Solving the Schrödinger Equation [0.0]
  A fundamental challenge lies in approximating the unitary evolution operator ( e-imathcalHt ) where ( mathcalH ) is a large, typically non-commuting, Hermitian operator.<n>We present a refinement of the fixed-depth simulation framework introduced by E. K"okc"u et al, incorporating the second-order Zassenhaus expansion.<n>This yields a controlled, non-unitary approximation with error scaling as ( mathcalO(t
  arXiv  Detail & Related papers  (2025-05-14T14:48:47Z)
• Few-fermion resonant tunneling and underbarrier trapping in asymmetric potentials [0.0]
  We investigate the tunneling dynamics of few-fermion systems in lattices under asymmetric external potentials. Our results may be applied to the design of nanoscale devices with tailored transport properties, such as diodes and memristors.
  arXiv  Detail & Related papers  (2024-12-04T17:36:07Z)
• Analytical Study of the Non-Hermitian Semiclassical Rabi Model [0.6554326244334868]
  The $mathcalPT$-broken phase closely matches the numerical exact one over a wide range of atomic frequencies. By analyzing the dynamics of excited-state population, we observe several stable oscillations in the Fourier spectrum. The present analytical treatment provides a concise and accurate description of the main physics of this non-Hermitian atom-field interaction system.
  arXiv  Detail & Related papers  (2024-12-04T00:08:45Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Many-body tunneling in a double-well potential [0.0]
  We present a novel approach for evaluating Wannier functions, offering a new perspective on their role in many-body systems. We address nonstandard Hubbard terms and demonstrate their critical influence on many-body dynamics. Our findings have important implications for phenomena like superconductivity in twisted bilayer graphene and metal-insulator transitions.
  arXiv  Detail & Related papers  (2024-09-06T14:36:31Z)
• Certifying nonlocal properties of noisy quantum operations [0.0]
  We provide a unified framework to certify nonlocal properties of quantum channels from the correlations obtained in measurement protocols. We study the effect of different models of dephasing noise, some of which are shown to generate nonlocality and entanglement in special cases.
  arXiv  Detail & Related papers  (2024-07-02T18:00:06Z)
• Score matching for sub-Riemannian bridge sampling [2.048226951354646]
  Recent progress in machine learning can be modified to allow training of score approximators on sub-Riemannian gradients. We perform numerical experiments exemplifying samples from the bridge process on the Heisenberg group and the concentration of this process for small time.
  arXiv  Detail & Related papers  (2024-04-23T17:45:53Z)
• Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processes [57.396578974401734]
  We introduce a principled framework for building a generative diffusion process on general manifold. Instead of following the denoising approach of previous diffusion models, we construct a diffusion process using a mixture of bridge processes. We develop a geometric understanding of the mixture process, deriving the drift as a weighted mean of tangent directions to the data points.
  arXiv  Detail & Related papers  (2023-10-11T06:04:40Z)
• Dilute neutron star matter from neural-network quantum states [58.720142291102135]
  Low-density neutron matter is characterized by the formation of Cooper pairs and the onset of superfluidity. We model this density regime by capitalizing on the expressivity of the hidden-nucleon neural-network quantum states combined with variational Monte Carlo and reconfiguration techniques.
  arXiv  Detail & Related papers  (2022-12-08T17:55:25Z)
• 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)
• Random-Matrix Approach to Transition-State Theory [0.0]
  We calculate the average probability for transition from scattering channel coupled to the first Hamiltonian to a scattering channel coupled to the second Hamiltonian. For tunneling through a very thick barrier independence of formation and decay of the tunneling process hold more generally.
  arXiv  Detail & Related papers  (2022-02-10T09:13:54Z)
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach [51.819912248960804]
  We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
  arXiv  Detail & Related papers  (2021-03-12T13:16:18Z)
• Kernel and Rich Regimes in Overparametrized Models [69.40899443842443]
  We show that gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. We also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.
  arXiv  Detail & Related papers  (2020-02-20T15:43:02Z)
• Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences [77.68028443709338]
  We propose a fully Bayesian formulation of the Epidemic Type Aftershock Sequence (ETAS) model. The occurrence of the mainshock earthquakes in a geographical region is assumed to follow an inhomogeneous spatial point process.
  arXiv  Detail & Related papers  (2020-02-05T10:11:26Z)

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.