Quantum
Mechanical Tunneling| 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 nonzero probability of being found on the other side later.
@ References: Burgess AJP(91)nov
[imaginary t];
Cushing FP(95);
Leavens FP(95);
Merzbacher PT(02)aug
[history]; Razavy 03 [r PT(04)feb];
Nimtz & Haibel 08.
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.
* 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);
Palao et al PLA(97)qp/99 [measurement];
Abolhasani & Golshani qp/99;
Yamada PRL(99);
Zhou et al PLA(01)
[phase transition to crossover]; 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);
Winful et al PRA(04)
[Dirac particles]; Davies AJP(05)jan-qp/04 [clock
model]; Chuprikov qp/05 [comparison
between defs]; 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].
@ 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 a0708-in.
Other Related Topics > s.a. experiments; instantons; quantum
equivalence principle.
@ 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].
@ 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].
@ Apparent superluminality: Krekora et al PRA(01);
Sokolovski & Liu PRA(01)
[semiclassical]; Winful PRL(03);
Sokolovski PRS(04)qp/03.
@ Other related topics: Aharonov et al PRA(93)
[penetration into classically
forbidden regions]; Eddi et al PRL(09) [analog in classical-wave + particle association].
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send feedback and suggestions to bombelli at olemiss.edu – modified 12
aug 2009