ON THE SURFACE WAVE ARISING AFTER DELOCALIZATION OF A QUANTUM PARTICLE IN THE COURSE OF ADIABATIC EVOLUTION

Standard

ON THE SURFACE WAVE ARISING AFTER DELOCALIZATION OF A QUANTUM PARTICLE IN THE COURSE OF ADIABATIC EVOLUTION. / Sergeev, V.A.; Fedotov, A.A.

в: St. Petersburg Mathematical Journal, Том 36, № 1, 2025, стр. 147-167.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{620ff1930a7a4b939e250898ff66318b,

title = "ON THE SURFACE WAVE ARISING AFTER DELOCALIZATION OF A QUANTUM PARTICLE IN THE COURSE OF ADIABATIC EVOLUTION",

abstract = "A one-dimensional nonstationary Schr{\"o}dinger equation is studied in the adiabatic approximation. The corresponding stationary operator, which depends on time as on a parameter, has a continuous spectrum filling the positive half-line and a finite number of negative eigenvalues. Over time, the eigenvalues approach the edge of the continuous spectrum and disappear one by one. A solution is studied that is close at some moment to an eigenfunction of the stationary operator. As long as the corresponding eigenvalue exists, this solution is localized inside the potential well. In a previous paper, the authors described its delocalization happening when the eigenvalue disappears. This paper describes the effects that occur after delocalization. {\textcopyright} 2025 American Mathematical Society",

keywords = "adiabatic evolution, delocalization of a quantum state, One-dimensional nonstationary Schr{\"o}dinger operator, surface wave",

author = "V.A. Sergeev and A.A. Fedotov",

note = "Export Date: 05 February 2026; Cited By: 1",

year = "2025",

doi = "10.1090/spmj/1851",

language = "Английский",

volume = "36",

pages = "147--167",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "1",

}

RIS

TY - JOUR

T1 - ON THE SURFACE WAVE ARISING AFTER DELOCALIZATION OF A QUANTUM PARTICLE IN THE COURSE OF ADIABATIC EVOLUTION

AU - Sergeev, V.A.

AU - Fedotov, A.A.

N1 - Export Date: 05 February 2026; Cited By: 1

PY - 2025

Y1 - 2025

N2 - A one-dimensional nonstationary Schrödinger equation is studied in the adiabatic approximation. The corresponding stationary operator, which depends on time as on a parameter, has a continuous spectrum filling the positive half-line and a finite number of negative eigenvalues. Over time, the eigenvalues approach the edge of the continuous spectrum and disappear one by one. A solution is studied that is close at some moment to an eigenfunction of the stationary operator. As long as the corresponding eigenvalue exists, this solution is localized inside the potential well. In a previous paper, the authors described its delocalization happening when the eigenvalue disappears. This paper describes the effects that occur after delocalization. © 2025 American Mathematical Society

AB - A one-dimensional nonstationary Schrödinger equation is studied in the adiabatic approximation. The corresponding stationary operator, which depends on time as on a parameter, has a continuous spectrum filling the positive half-line and a finite number of negative eigenvalues. Over time, the eigenvalues approach the edge of the continuous spectrum and disappear one by one. A solution is studied that is close at some moment to an eigenfunction of the stationary operator. As long as the corresponding eigenvalue exists, this solution is localized inside the potential well. In a previous paper, the authors described its delocalization happening when the eigenvalue disappears. This paper describes the effects that occur after delocalization. © 2025 American Mathematical Society

KW - adiabatic evolution

KW - delocalization of a quantum state

KW - One-dimensional nonstationary Schrödinger operator

KW - surface wave

U2 - 10.1090/spmj/1851

DO - 10.1090/spmj/1851

M3 - статья

VL - 36

SP - 147

EP - 167

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 1

ER -

ID: 149073775