dorsal/arxiv
View SchemaMore About Tunnelling Times, the Dwell Time, and the ``Hartman Effect"
| Authors | V. S. Olkhovsky, E. Recami, F. Raciti, A. Zaichenko |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9508010 |
| URL | https://arxiv.org/abs/quant-ph/9508010 |
| DOI | 10.1051/jp1:1995202 |
Abstract
In a recent review paper [{\em Phys. Reports} {\bf 214} (1992) 339] we proposed, within conventional quantum mechanics, new definitions for the sub-barrier tunnelling and reflection times. \ Aims of the present paper are: \ (i) presenting and analysing the results of various numerical calculations (based on our equations) on the penetration and return times $<\tau_{\, \rm Pen}>$, $<\tau_{\, \rm Ret}>$, during tunnelling {\em inside} a rectangular potential barrier, for various penetration depths $x_{\rm f}$; \ (ii) putting forth and discussing suitable definitions, besides of the mean values, also of the {\em variances} (or dispersions) ${\rm D} \, {\tau_{\rm T}}$ and ${\rm D} \, {\tau_{\, \rm R}}$ for the time durations of transmission and reflection processes; \ (iii) mentioning, moreover, that our definition $<\tau_{\rm T}>$ for the average transmission time results to constitute an {\em improvement} of the ordinary dwell--time ${\ove \tau}^{\rm Dw}$ formula: \ (iv) commenting, at last, on the basis of our {\em new} numerical results, upon some recent criticism by C.R.Leavens. \ \ We stress that our numerical evaluations {\em confirm} that our approach implied, and implies, the existence of the {\em Hartman effect}: an effect that in these days (due to the theoretical connections between tunnelling and evanescent--wave propagation) is receiving ---at Cologne, Berkeley, Florence and Vienna--- indirect, but quite interesting, experimental verifications. \ Eventually, we briefly analyze some other definitions of tunnelling times.
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"abstract": "In a recent review paper [{\\em Phys. Reports} {\\bf 214} (1992) 339] we\nproposed, within conventional quantum mechanics, new definitions for the\nsub-barrier tunnelling and reflection times. \\ Aims of the present paper are: \\\n(i) presenting and analysing the results of various numerical calculations\n(based on our equations) on the penetration and return times $\u003c\\tau_{\\, \\rm\nPen}\u003e$, $\u003c\\tau_{\\, \\rm Ret}\u003e$, during tunnelling {\\em inside} a rectangular\npotential barrier, for various penetration depths $x_{\\rm f}$; \\ (ii) putting\nforth and discussing suitable definitions, besides of the mean values, also of\nthe {\\em variances} (or dispersions) ${\\rm D} \\, {\\tau_{\\rm T}}$ and ${\\rm D}\n\\, {\\tau_{\\, \\rm R}}$ for the time durations of transmission and reflection\nprocesses; \\ (iii) mentioning, moreover, that our definition $\u003c\\tau_{\\rm T}\u003e$\nfor the average transmission time results to constitute an {\\em improvement} of\nthe ordinary dwell--time ${\\ove \\tau}^{\\rm Dw}$ formula: \\ (iv) commenting, at\nlast, on the basis of our {\\em new} numerical results, upon some recent\ncriticism by C.R.Leavens. \\ \\ We stress that our numerical evaluations {\\em\nconfirm} that our approach implied, and implies, the existence of the {\\em\nHartman effect}: an effect that in these days (due to the theoretical\nconnections between tunnelling and evanescent--wave propagation) is receiving\n---at Cologne, Berkeley, Florence and Vienna--- indirect, but quite\ninteresting, experimental verifications. \\ Eventually, we briefly analyze some\nother definitions of tunnelling times.",
"arxiv_id": "quant-ph/9508010",
"authors": [
"V. S. Olkhovsky",
"E. Recami",
"F. Raciti",
"A. Zaichenko"
],
"categories": [
"quant-ph",
"cond-mat"
],
"doi": "10.1051/jp1:1995202",
"title": "More About Tunnelling Times, the Dwell Time, and the ``Hartman Effect\"",
"url": "https://arxiv.org/abs/quant-ph/9508010"
},
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