Quantum effects and quantum chaos in multidimensional tunneling

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10367391" target="_blank" >RIV/00216208:11320/17:10367391 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1103/PhysRevE.96.062201" target="_blank" >http://dx.doi.org/10.1103/PhysRevE.96.062201</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevE.96.062201" target="_blank" >10.1103/PhysRevE.96.062201</a>

Result language

angličtina

Original language name

Quantum effects and quantum chaos in multidimensional tunneling

Original language description

The ground-state energy splitting due to tunneling in two-dimensional double wells of the form V (x, y) = (x(2) - R-2)(2)/8R(2) + x(2) - R-2/R-2 gamma y +omega(2)/2 y(2) is calculated. Several results are reported. First, we give a systematic WKB expansion of the splitting in series in powers of R-2, each term of the series being a finite polynomial in gamma(2). We find an ascending sequence of the values of the parameter. characterizing the curvature of the classical path, for which the successive corrections to the leading order vanish. This effect arises because curvature of the path and quantum nature of motion cancel each other; it does not appear for one-dimensional double wells. Second, we find that for large curvatures, such as for those describing the proton transfer in a malonaldehyde and hydroxalate anion, this expansion is of no practical use. Thus, the WKB expansion is reordered to a strong coupling form, each term of the series in powers of R-2 being an infinite series in powers of (gamma) over bar (2), (gamma) over bar = gamma/R. Third, we find that the radius of convergence of the series is determined by the singularity at (gamma) over bars = omega/2. At the singularity the system changes its character from being a double well to become a single well. Close to this singularity the classical action and its first quantum correction are found to be nonanalytic functions of gamma, most likely of the form [1 - ((gamma) over bar/(gamma) over bars)(2)](alpha), where alpha = 1/2 and alpha = - 1/2 for the classical action and its first quantum correction, respectively. Since in the semiclassical regime of large R the splitting is exponentially dependent on the value of the classical action and its first quantum correction, close to the singularity we establish strong sensitivity of the splitting on slight variations of the parameter. (gamma) over bar entering the Hamiltonian linearly.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10300 - Physical sciences

Project

<a href="/en/project/GA16-06240S" target="_blank" >GA16-06240S: Structure and dynamics of organometallic complexes in bio-environment.</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Physical Review E

ISSN

2470-0045

e-ISSN

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Volume of the periodical

96

Issue of the periodical within the volume

6

Country of publishing house

US - UNITED STATES

Number of pages

7

Pages from-to

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UT code for WoS article

000416850600006

EID of the result in the Scopus database

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