GEOMETRIC PHASES OF PURE AND MIXED STATES

COSMOS ◽  
2006 ◽  
Vol 02 (01) ◽  
pp. 81-100
Author(s):  
R. RAVISHANKAR ◽  
J. F. DU
Keyword(s):  
Experimental Measurement ◽  
Mixed State ◽  
Geometric Phase ◽  
Mixed States ◽  
Geometric Phases

The purpose of this article is to review the literature for pure and mixed state geometric phase and also the experimental measurement of the phase using NMR.

scholarly journals Sub-Geometric Phases in Density Matrices

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Zheng-Chuan Wang
Keyword(s):  
Mixed State ◽  
Geometric Phase ◽  
Density Matrices ◽  
Geometric Phases

Abstract This study presents the generalization of geometric phases in density matrices. We show that the extended sub-geometric phase has an unified expression during the adiabatic or nonadiabatic process and establish the relations between them and the usual Berry or Aharonov-Anandan phases. We also demonstrate the influence of sub-geometric phases on the physical observables. Finally, the above treatment is used to investigate the geometric phase in a mixed state.

scholarly journals Geometric phases for mixed states of the Kitaev chain

2016 ◽  
Vol 374 (2068) ◽  
pp. 20150231 ◽  
Author(s):  
Ole Andersson ◽  
Ingemar Bengtsson ◽  
Marie Ericsson ◽  
Erik Sjöqvist
Keyword(s):  
Finite Temperature ◽  
Geometric Phase ◽  
Berry Phase ◽  
Condensed Matter ◽  
Order Parameters ◽  
Topological Order ◽  
Mixed States ◽  
Geometric Phases

The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyse the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation.

scholarly journals GEOMETRY OF DECOMPOSITION DEPENDENT EVOLUTIONS OF MIXED STATES

2004 ◽  
Vol 02 (02) ◽  
pp. 247-256 ◽  
Author(s):  
DAVID KULT ◽  
ERIK SJÖQVIST
Keyword(s):  
Mixed State ◽  
Geometric Phase ◽  
Parallel Transport ◽  
Mixed States ◽  
Completely Positive Maps ◽  
Completely Positive ◽  
Positive Maps

We examine evolutions where each component of a given decomposition of a mixed quantal state evolves independently in a unitary fashion. The geometric phase and parallel transport conditions for this type of decomposition dependent evolution are delineated. We compare this geometric phase with those previously defined for unitarily evolving mixed states, and mixed state evolutions governed by completely positive maps.

scholarly journals Vacuum Condensate, Geometric Phase, Unruh Effect, and Temperature Measurement

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Antonio Capolupo ◽  
Giuseppe Vitiello
Keyword(s):  
Temperature Measurement ◽  
Mixed State ◽  
Geometric Phase ◽  
Thermal State ◽  
External Potential ◽  
Unruh Effect ◽  
Vacuum Condensate ◽  
Geometric Phases ◽  
Vacuum Condensation ◽  
Thermal States

In our previous work the possibility to use the Aharonov-Anandan invariant as a tool in the analysis of disparate systems has been shown, including Hawking and Unruh effects, as well as graphene physics and thermal states. We show that the vacuum condensation, characterizing such systems, is also related with geometric phases and we analyze the properties of the geometric phase of systems represented by mixed state and undergoing a nonunitary evolution. In particular, we consider two-level atoms accelerated by an external potential and interacting with a thermal state. We propose the realization of Mach-Zehnder interferometers which can prove the existence of the Unruh effect and can allow very precise measurements of temperature.

The treatment of mixed states and the risk of switching to depression

2005 ◽  
Vol 20 (2) ◽  
pp. 96-100 ◽  
Author(s):  
Eduard Vieta
Keyword(s):  
Clinical Trials ◽  
Depressive Symptoms ◽  
Mixed State ◽  
Atypical Antipsychotics ◽  
Randomized Clinical Trials ◽  
Mixed States ◽  
Conventional Antipsychotics

AbstractThere are few controlled studies evaluating the treatment of bipolar mixed states. Evidence suggests that mixed states may be more responsive to some anticonvulsants than to lithium. Olanzapine alone or in combination with divalproate or lithium has been adequately evaluated in randomized clinical trials involving mixed-state patients, whereas risperidone and quetiapine have not. There is also some evidence demonstrating the efficacy of ziprasidone and aripiprazole. The risk of switching to depression is high in mixed states. Conventional antipsychotics, such as haloperidol, may be less efficacious at protecting against a switch to depression than atypical antipsychotics, divalproate or lithium. When choosing drugs for the treatment of mania, and especially for the treatment of mixed states, their efficacy against manic and depressive symptoms, and their safety in terms of the risk of switching to depression should be taken into account.

scholarly journals Geometric phases for mixed states during cyclic evolutions

2004 ◽  
Vol 37 (11) ◽  
pp. 3699-3705 ◽  
Author(s):  
Li-Bin Fu ◽  
Jing-Ling Chen
Keyword(s):  
Mixed States ◽  
Geometric Phases

scholarly journals Virtual Correlations in Single Qutrit

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Alexey A. Strakhov ◽  
Vladimir I. Man’ko
Keyword(s):  
Mixed State ◽  
Three Dimensional ◽  
Mixed States ◽  
One To One

We construct the positive invertible map of the mixed states of a single qutrit onto the antisymmetrized bipartite qutrit states (quasifermions). It is shown that using this one-to-one correspondence between qutrit states and states of two three-dimensional quasifermions one may attribute hidden entanglement to a single mixed state of qutrit.

scholarly journals GEOMETRIC PHASES AND QUANTUM PHASE TRANSITIONS

2008 ◽  
Vol 22 (06) ◽  
pp. 561-581 ◽  
Author(s):  
SHI-LIANG ZHU
Keyword(s):  
Phase Transitions ◽  
Geometric Phase ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Quantum Phase ◽  
Many Body ◽  
Scientific Communities ◽  
Geometric Phases ◽  
Many Body Systems ◽  
The Many

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities.

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