Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach

被引：4

作者：

Pilatowsky-Cameo, Saul ^{[1
,2
]}

Villasenor, David ^{[1
]}

Bastarrachea-Magnani, Miguel A. ^{[3
]}

Lerma-Hernandez, Sergio ^{[4
]}

Hirsch, Jorge G. ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Ciencias Nucl, Apdo Postal 70-543, Cdmx 04510, Mexico

[2] MIT, Ctr Theoret Phys, Cambridge, MA 02139 USA

[3] Univ Autonoma Metropolitana Iztapalapa, Dept Fis, San Rafael Atlixco 186, Cdmx 09340, Mexico

[4] Univ Veracruzana, Fac Fis, Circuito Aguirre Beltran S-N, Xalapa 91000, Veracruz, Mexico

来源：

PHYSICAL REVIEW E | 2022年 / 105卷 / 06期

关键词：

TIME DEVELOPMENT; QUANTUM; CHAOS; TRANSITION; SYSTEMS; SCARS;

D O I：

10.1103/PhysRevE.105.064209

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite-dimensional Hilbert space. We compare our general expressions with numerical results for the spin-boson Dicke model in the chaotic energy regime, restricting its unbounded four-dimensional phase space to a classically chaotic energy shell. This effective dimension can be employed to characterize quantum phenomena in infinite-dimensional systems, such as localization and scarring.

引用

页数：11

共 41 条

[1] Chaos in the Dicke model: quantum and semiclassical analysis [J].

Angel Bastarrachea-Magnani, Miguel ;

Lopez-del-Carpio, Baldemar ;

Lerma-Hernandez, Sergio ;

Hirsch, Jorge G. .

PHYSICA SCRIPTA, 2015, 90 (06)

[2]

Bargmann V., 1971, Reports on Mathematical Physics, V2, P221, DOI 10.1016/0034-4877(71)90006-1

[3] Comparative quantum and semiclassical analysis of atom-field systems. I. Density of states and excited-state quantum phase transitions [J].

Bastarrachea-Magnani, M. A. ;

Lerma-Hernandez, S. ;

Hirsch, J. G. .

PHYSICAL REVIEW A, 2014, 89 (03)

[4] Comparative quantum and semiclassical analysis of atom-field systems. II. Chaos and regularity [J].

Bastarrachea-Magnani, M. A. ;

Lerma-Hernandez, S. ;

Hirsch, J. G. .

PHYSICAL REVIEW A, 2014, 89 (03)

[5] Classical chaos in atom-field systems [J].

Chavez-Carlos, J. ;

Bastarrachea-Magnani, M. A. ;

Lerma-Hernandez, S. ;

Hirsch, J. G. .

PHYSICAL REVIEW E, 2016, 94 (02)

[6] Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems [J].

Chavez-Carlos, Jorge ;

Lopez-del-Carpio, B. ;

Bastarrachea-Magnani, Miguel A. ;

Stransky, Pavel ;

Lerma-Hernandez, Sergio ;

Santos, Lea F. ;

Hirsch, Jorge G. .

PHYSICAL REVIEW LETTERS, 2019, 122 (02)

[7] CHAOS IN A SPIN BOSON SYSTEM - CLASSICAL-ANALYSIS [J].

DEAGUIAR, MAM ;

FURUYA, K ;

LEWENKOPF, CH ;

NEMES, MC .

ANNALS OF PHYSICS, 1992, 216 (02) :291-312

[8] PARTICLE-SPIN COUPLING IN A CHAOTIC SYSTEM - LOCALIZATION-DELOCALIZATION IN THE HUSIMI DISTRIBUTIONS [J].

DEAGUIAR, MAM ;

FURUYA, K ;

LEWENKOPF, CH ;

NEMES, MC .

EUROPHYSICS LETTERS, 1991, 15 (02) :125-131

[9] COHERENCE IN SPONTANEOUS RADIATION PROCESSES [J].

DICKE, RH .

PHYSICAL REVIEW, 1954, 93 (01) :99-110

[10] Chaos and the quantum phase transition in the Dicke model [J].

Emary, C ;

Brandes, T .

PHYSICAL REVIEW E, 2003, 67 (06) :22-066203

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