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Universal Probability Distribution for the Wave Function of a Quantum System Entangled with Its Environment

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TypeOfResource
Text
TitleInfo
Title
Universal Probability Distribution for the Wave Function of a Quantum System Entangled with Its Environment
Name (type = personal)
NamePart (type = family)
Goldstein
NamePart (type = given)
Sheldon
Affiliation
Mathematics, Rutgers University
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Lebowitz
NamePart (type = given)
Joel L.
Affiliation
Mathematics, Rutgers University
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Mastrodonato
NamePart (type = given)
Christian
Affiliation
University of Genoa
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (authority = orcid); (authorityURI = http://id.loc.gov/vocabulary/identifiers/orcid.html); (type = personal); (valueURI = http://orcid.org/0000-0001-5075-9929)
NamePart (type = family)
Tumulka
NamePart (type = given)
Roderich
Affiliation
Mathematics, Rutgers University
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Zanghì
NamePart (type = given)
Nino
Affiliation
University of Genoa
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (authority = RutgersOrg-Department); (type = corporate)
NamePart
Mathematics
Name (authority = RutgersOrg-School); (type = corporate)
NamePart
School of Arts and Sciences (SAS) (New Brunswick)
Genre (authority = RULIB-FS)
Article, Refereed
Genre (authority = NISO JAV)
Accepted Manuscript (AM)
Note (type = peerReview)
Peer reviewed
OriginInfo
DateCreated (encoding = w3cdtf); (keyDate = no); (qualifier = exact)
2015
Publisher
Springer
DateIssued (encoding = w3cdtf); (keyDate = yes)
2016
Abstract (type = Abstract)
A quantum system (with Hilbert space H1) entangled with its environment (with Hilbert space H2) is usually not attributed a wave function but only a reduced density matrix ρ1. Nevertheless, there is a precise way of attributing to it a random wave function ψ1, called its conditional wave function, whose probability distribution μ1 depends on the entangled wave function ψ∈H1⊗H2 in the Hilbert space of system and environment together. It also depends on a choice of orthonormal basis of H2 but in relevant cases, as we show, not very much. We prove several universality (or typicality) results about μ1, e.g., that if the environment is sufficiently large then for every orthonormal basis of H2, most entangled states ψ with given reduced density matrix ρ1 are such that μ1 is close to one of the so-called GAP (Gaussian adjusted projected) measures, GAP(ρ1). We also show that, for most entangled states ψ from a microcanonical subspace (spanned by the eigenvectors of the Hamiltonian with energies in a narrow interval [E,E+δE]) and most orthonormal bases of H2, μ1 is close to GAP(tr2ρmc) with ρmc the normalized projection to the microcanonical subspace. In particular, if the coupling between the system and the environment is weak, then μ1 is close to GAP(ρβ) with ρβ the canonical density matrix on H1 at inverse temperature β=β(E). This provides the mathematical justification of our claim in [J. Statist. Phys. 125:1193 (2006), http://arxiv.org/abs/quant-ph/0309021] that GAP measures describe the thermal equilibrium distribution of the wave function.
Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
PhysicalDescription
InternetMediaType
application/pdf
Extent
27 p.
Subject (authority = LCSH)
Topic
Gaussian measures
Subject (authority = local)
Topic
Gaussian adjusted projected (GAP) measures
Subject (authority = local)
Topic
Scrooge measures
Subject (authority = local)
Topic
Haar measure on the unitary group
Subject (authority = local)
Topic
Thermodynamic limit
Subject (authority = local)
Topic
Canonical ensemble in quantum mechanics
Subject (authority = local)
Topic
Typicality theorems
Subject (authority = local)
Topic
Conditional wave function
Subject (authority = local)
Topic
Typical wave function
Subject (authority = LCSH)
Topic
Wave functions
Extension
DescriptiveEvent
Type
Citation
AssociatedObject
Name
Communications in Mathematical Physics
Type
Journal
Relationship
Has part
Reference (type = url)
http://dx.doi.org/10.1007/s00220-015-2536-0
Identifier (type = volume and issue)
342(3)
Detail
965-988
DateTime (encoding = w3cdtf)
2016
Extension
DescriptiveEvent
Type
Grant award
AssociatedEntity
Role
Funder
Name
National Science Foundation
AssociatedEntity
Role
Originator
Name
Sheldon Goldstein
AssociatedObject
Type
Grant number
Name
DMS-0504504
Extension
DescriptiveEvent
Type
Grant award
AssociatedEntity
Role
Funder
Name
National Science Foundation
AssociatedEntity
Role
Originator
Name
Joel Lebowitz
AssociatedObject
Type
Grant number
Name
DMR 08-02120
Extension
DescriptiveEvent
Type
Grant award
AssociatedEntity
Role
Funder
Name
Air Force Office of Scientific Research
AssociatedEntity
Role
Originator
Name
Joel Lebowitz
AssociatedObject
Type
Grant number
Name
AF-FA 49620-01-0154
Extension
DescriptiveEvent
Type
Grant award
AssociatedEntity
Role
Funder
Name
Istituto Nazionale di Fisica Nucleare
AssociatedEntity
Role
Originator
Name
Nino Zanghi
RelatedItem (type = host)
TitleInfo
Title
Goldstein, Sheldon
Identifier (type = local)
rucore30189300001
RelatedItem (type = host)
TitleInfo
Title
Lebowitz, Joel L.
Identifier (type = local)
rucore30189200001
RelatedItem (type = host)
TitleInfo
Title
Tumulka, Roderich
Identifier (type = local)
rucore30181500001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3MS3VQH
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Copyright for scholarly resources published in RUcore is retained by the copyright holder. By virtue of its appearance in this open access medium, you are free to use this resource, with proper attribution, in educational and other non-commercial settings. Other uses, such as reproduction or republication, may require the permission of the copyright holder.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
RightsEvent
Type
Permission or license
AssociatedObject
Type
License
Name
Multiple author license v. 1
Detail
I hereby grant to Rutgers, The State University of New Jersey (Rutgers) the non-exclusive right to retain, reproduce, and distribute the deposited work (Work) in whole or in part, in and from its electronic format, without fee. This agreement does not represent a transfer of copyright to Rutgers. Rutgers may make and keep more than one copy of the Work for purposes of security, backup, preservation, and access and may migrate the Work to any medium or format for the purpose of preservation and access in the future. Rutgers will not make any alteration, other than as allowed by this agreement, to the Work. I represent and warrant to Rutgers that the Work is my original work. I also represent that the Work does not, to the best of my knowledge, infringe or violate any rights of others. I further represent and warrant that I have obtained all necessary rights to permit Rutgers to reproduce and distribute the Work and that any third-party owned content is clearly identified and acknowledged within the Work. By granting this license, I acknowledge that I have read and agreed to the terms of this agreement and all related RUcore and Rutgers policies.
RightsEvent
Type
Embargo
DateTime (encoding = w3cdtf); (point = start)
2015-12-03
DateTime (encoding = w3cdtf); (point = end)
2017-05-01
Detail
Access to this PDF has been restricted at the publisher's request. The publisher, Springer Verlag, requires a 12 month embargo from the date the article was published. The article in this repository will be publicly available after May 1, 2017.
RightsHolder (type = corporate)
Name
Springer
Role
Copyright holder
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ContentModel
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