Quantum Statistical Mechanical States| Quantum Statistical Mechanical States |
In General \ s.a. quantum statistical mechanics.
* Quantum microcanonical postulate:
A modification of the microcanonical postulate according to which for a
system in microcanonical equilibrium all pure quantum states having the
same energy expectation value are realised with equal probability.
$ Microcanonical state:
The density matrix ρ = δ(H−E)
/ tr[δ(H−E)], for some fixed value
E of the energy.
* Schrödinger-Park paradox:
A fundamental difficulty undermining the concept of individual "state" in the
present formulations of quantum statistical mechanics (and in its quantum
information theory interpretation as well), which is an unavoidable consequence
of an observation by Schrödinger and Park; To resolve it, we must either
reject as unsound the concept of state, or reformulate quantum theory and the
role of statistics in it.
@ Equilibrium states: Linden et al NJP(10)-a0907 [speed of fluctuations];
Goldstein et al PRL(15)-a1506 [pure states, macroscopic vs microscopic thermal equilibrium];
Goldstein et al AdP(17)-a1610 [macroscopic vs microscopic thermal equilibrium];
> s.a. equilibrium [thermalization].
@ Distribution functions:
Lee PRP(95);
Lukkarinen JPA(00) [non-canonical];
Pandya & Tumulka JSP(14)-a1306 [canonical].
@ Microcanonical state:
Brody et al qp/05 [equilibrium],
PRS(07)qp/05 [finite-dimensional Hilbert space, phase transition],
JPCS(07)qp/06 [and grand microcanonical ensemble];
Bender et al JPA(05)qp;
Naudts & Van der Straeten JSM(06)qp [alternative definition];
Sugita NPCS(07)cm/06 [basis for use];
> s.a. foundations of quantum theory.
@ Grand canonical ensemble: Brody et al JPA(07)qp
[ergodic theorem, unitary evolution of closed quantum systems leads to grand canonical ensemble];
Zannetti EPL(15)-a1507 [grand canonical catastrophe and condensation of fluctuations].
Related topics: see mixed
states; phase-space formulation and wigner
functions; states in statistical mechanics.
Canonical Ensemble, Thermal State
> s.a. equilibrium [thermalization].
$ Canonical partition function:
The function Z = tr exp{–βH} (Z
stands for "Zustandsumme"; Q is another common symbol); Its
value is a measure of the number of states effectively available to the
system at temperature β and for a given set of values for
the parameters in the Hamiltonian H.
@ General references: Brody & Hughston JMP(98)qp/97,
JMP(99)qp/97;
Tasaki PRL(98) [from quantum dynamics];
Albeverio et al TMMS-m.PR/05 [estimates for quantum lattice systems];
Goldstein et al PRL(06) [from pure state of system + bath];
Gu PS(10) [decomposition];
Seglar & Pérez EJP(13) [classical limit];
Magnus & Brosens a1505 [projection operator approach for the partition function];
Perarnau-Llobet et al NJP(16)-a1512
[generalised Gibbs ensembles, work and entropy production];
Kliesch & Riera a1803-in [locality of temperature, decay of correlations];
Ozorio de Almeida et al a2009 [in phase space];
Nicacio a2012 [Weyl-Wigner representation].
@ Thermal pure quantum states:
Sugiura & Shimizu PRL(12)-a1112,
PRL(13)-a1302;
Sugiura & Shimizu a1312-proc;
Hyuga et al PRB(14)-a1405 [infinite-dimensional Hilbert spaces];
Kaufman et al Sci(16)aug-a1603 [local thermalization of a globally pure state];
Dymarsky & Liu PRE(19)-a1702 [universality of (approximately) canonical states].
@ Eigenstate thermalization hypothesis:
Chandran et al PRA(16)-a1607 [constrained Hilbert spaces];
Shiraishi & Mori PRL(17)-a1702,
comment Mondaini et al a1711 [counterexamples];
Musumbu et al a1703 [discrete time quantum walk simulations on lattices];
Lan & Powell PRB(17)-a1706 [in quantum dimer models];
Deutsch RPP(18)-a1805 [rev];
Murthy & Srednicki PRL-a1906 [bounds on chaos];
Erdős et al a2012 [for Wigner matrices].
@ Schrödinger-Park paradox: Beretta MPLA(06)qp [and the Hatsopoulos-Gyftopoulos proposal];
> s.a. Paradoxes.
@ Related topics: Cunden et al JPA(13)-a1304 [polarized ensembles of random pure states];
Alonso et al PRE-a1403 [ensemble leading to non-extensive thermodynamic functions].
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