Quantum Mechanical Tunneling  

In General > s.a. WKB Approximation.
* Idea: A particle whose wave function is initially localized on one side of a potential barrier, with energy less that the maximum value of the barrier, has a non-zero probability of being found on the other side later.
@ References: Burgess AJP(91)nov [imaginary time]; Cushing FP(95); Leavens FP(95); Merzbacher PT(02)aug [history]; Nimtz & Haibel 08; Razavy 14 [e1 r PT(04)feb]; news guardian(14)oct [how it works].
> Examples: see boundary conditions in quantum cosmology.

Tunneling Time > s.a. causality violations.
* Time scale: For thin barriers, the tunneling time is linear in the width; For thicker ones, it saturates (Hartman effect) and there is a time scale associated with it; What does it mean? The tunneling speed is usually characterized by the Wigner velocity, but there are other proposals; The group delay is proportional to the energy stored, and equal to the dwell time plus a self-interference delay.
* Measurement: It has been measured in experiments based on the attoclock in ultrafast laser ionization of Helium atoms.
* Remark: The transit time of a particle between two points is not necessarily well defined in standard quantum mechanics, whereas it is in Bohm's theory; For this reason tunneling times may allow us to test the pilot-wave approach by providing us with a situation in which Bohm's theory can make a definite prediction when standard quantum mechanics can make none.
@ General references: Fertig PRL(90) [distribution]; Chen & Wang PLA(90); Olkhovsky & Recami PRP(92); Landauer & Martin RMP(94); Leavens PLA(95); Steinberg PRL(95); Eisenberg & Ashkenazy FP(97)qp/96; Challinor et al PLA(97); Abolhasani & Golshani qp/99; Yamada PRL(99); Ruseckas PRA(01)qp; Chuprikov qp/01; de Carvalho & Nussenzveig PRP(02); Privitera et al RNC(03)qp/04 [intro]; Olkhovsky et al PRP(04); Wang et al PRA(04); Davies AJP(05)jan-qp/04 [clock model]; Chuprikov qp/05 [comparison between definitions]; Winful NJP(06)qp [meaning]; Wu a0804 [imaginary time]; Bernardini AP(09)-a0903 [and scattering delay time]; Nimtz a0903 [rev]; Ordóñez & Hatano PRA(09)-a0905 [non-existence of intrinsic tunneling time]; De Leo & Leonardi JPA(11)-a1103 [phase time formula]; Aichmann & Nimtz FP(14) [misleading interpretations]; Demir & Güner a1512 [entropic formulation].
@ Phase space approach: Marinov & Segev PRA(96); Xavier et al PRL(97) [semiclassical].
@ Hartman effect: Winful OE(02), PRL(03), PRP(06); Martínez & Polatdemir PLA(06); Winful SPIE(07)-a0708; Bhattacharya & Roy JMP(13) [precluded for dissipative systems]; > s.a. causality in quantum theory.
@ Measurements: Palao et al PLA(97)qp/99; Camus et al PRL(17)-a1611 + news sn(17)jul [evidence]; > s.a. experiments in quantum mechanics.
@ Related topics: Zhou et al PLA(01) [phase transition to crossover]; Winful et al PRA(04) [Dirac particles]; Xu et al FP(13) [relativistic extensions]; Bhattacharya PRA(14) [two-state particle tunneling through a thermal magnetic barrier]; Kelkar et al AP(17)-a1705 [with dissipation].

Related Topics > s.a. quantum chaos; quantum equivalence principle; wigner function.
@ Dynamics: Krekora et al PRA(01) [speed]; Delgado et al PRA(03); Faria et al FP(06) [Kramers escape rate theory]; Calzetta & Verdaguer JPA(06) [decoherence and anomalous diffusion]; Anastopoulos & Savvidou a1611 [quasi-classical paths].
@ Approaches: Olavo qp/96 [in classical interpretation of quantum mechanics]; Anastopoulos & Savvidou JMP(06)qp, JMP(08)-a0706, Anastopoulos JMP(08)-a0706 [as time-of-arrival problem, and decay]; Levkov et al PRL(07)-a0707 [semiclassical solutions]; Chuprikov a1303 [new approach]; Norsen AJP(13)apr [pilot-wave perspective]; Turok NJP(14)-a1312 [in real time, using complex classical trajectories]; Hipple a1411 ["tunneling" transform]; > s.a. Polymer Representation.
@ Apparent superluminality: Krekora et al PRA(01); Sokolovski & Liu PRA(01) [semiclassical]; Winful PRL(03); Sokolovski PRS(04)qp/03; Nimtz FP(11)-a1004 [violation of special relativity]; Aichmann & Nimtz a1304; Fayngold a1412.
@ Other related topics: Aharonov et al PRA(93) [penetration into classically forbidden regions]; Eddi et al PRL(09) [analog in classical-wave + particle association]; Bender & Hook JPA(11)-a1011 [classical analog for complex-energy particle]; Ivlev a1108 [penetration through classical barriers?]; > s.a. GUP phenomenology; instantons; quantum systems [tunneling in momentum space, potential step].


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