Entropic Tunneling Time and its Applications

Paolo Malgaretti, Francesco Petiziol, Alexander Schnell

Hakan ÜNAL

N. G. Kelkar, D. Lozano Gómez, Edgar J. Patiño

D. Demir, Tuğrul Güner

Quantum tunneling governs numerous phenomena in biology, chemistry, physics and technology. Tunneling time, formulated in various different forms due to the absence of a time operator in quantum theory, has been measured recently in experiments based on the attoclock in ultrafast laser ionization of Helium atoms [A.~Landsman {\it et al.}, Optica {\bf 1}, 343 (2014)]. The experiment performs a refined measurement with which no tunneling time formula in the literature exhibits adequate congruence. Here we show that, entropic considerations lead to a real tunneling time which shows remarkable agreement with the experimental data and stays always subluminal. Indeed, with phase space volume setting the number of microstates for a single evanescing particle in a state of definite momentum consistent with energy conservation, one is naturally led to a statistical description for quantum tunneling in which thermal energy sets the tunneling time. This entropic tunneling time is rather general and might also be extended to photon and phonon tunneling phenomena.

Matteo Bellitti, Federico Ricci‐Tersenghi, Antonello Scardicchio

We study both classical and quantum algorithms to solve a hard optimization problem, namely 3-XORSAT on 3-regular random graphs. By introducing a new quasi-greedy algorithm that is not allowed to jump over large energy barriers, we show that the problem hardness is mainly due to entropic barriers. We study, both analytically and numerically, several optimization algorithms, finding that entropic barriers affect in a similar way classical local algorithms and quantum annealing. For the adiabatic algorithm, the difficulty we identify is distinct from that of tunneling under large barriers, but does, nonetheless, give rise to exponential running (annealing) times.

Shimon Levit

We introduce a general variational framework to address the tunneling of hot Fermi systems. We use the representation of the trace of the imaginary time τ = i t propagator as a functional integral type of a sum over complete sets of states at intermediate propagation slices. We assume that these states are τ -dependent and generated by an arbitrary trial Hamiltonian H 0 ( τ ) . We then use the convexity inequality to derive H 0 ( τ ) controlled variational bound for a trial action functional. This functional has a general structure consisting of two parts - statistically weighted quantum penetrability and dynamical tunneling entropy. We examine how this structure incorporates the basic physics of tunneling of hot Fermi systems. Using the variational inequality one can optimise the dynamical parameters controlling the action functional for any choice of the trial problem. As an application we take H 0 ( τ ) to describe imaginary time dynamics of non interacting Bogoliubov-de Gennes (BdG) quasiparticles . Optimising its dynamical parameters we extend the tunneling theory of hot Fermi systems to the Hartree-Fock-Bogoliubov (HFB) frame and derive the corresponding generalisation of imaginary time temperature dependent BdG mean field equations. As in the trial action the prominent feature of these equations is an inseparable interplay between quantum dynamical and entropic statistical effects. In the zero temperature limit these equations describe the “false ground state” tunneling decay of superfluid Fermi systems (spontaneous fission in nuclear physics). With increasing excitation energy (effective temperature) the decay process is gradually evolving from pure quantum tunneling to statistical “bottle neck” escape mechanism. Correspondingly the statistically weighted dynamical penetrability part in the action gradually decreases while the tunneling entropy increases with increasing effective temperature.