Quantum effects and quantum chaos in multidimensional tunneling

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Quantum effects and quantum chaos in multidimensional tunneling

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Quantum effects and quantum chaos in multidimensional tunneling

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

<a href="/cs/project/GA16-06240S" target="_blank" >GA16-06240S: Struktura a dynamika organokovových komplexů v biologickém prostředí.</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Physical Review E

ISSN

2470-0045

e-ISSN

—

Svazek periodika

96

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

7

Strana od-do

—

Kód UT WoS článku

000416850600006

EID výsledku v databázi Scopus

—