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.

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.

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 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.

BERRY PHASE IN COUPLED TWO-LEVEL SYSTEMS

2013 ◽  
Vol 27 (12) ◽  
pp. 1350088 ◽  
Author(s):  
X. Y. ZHANG ◽  
J. H. TENG ◽  
X. X. YI
Keyword(s):  
Asymptotic Behavior ◽  
Geometric Phase ◽  
Berry Phase ◽  
External Control ◽  
Control Parameters ◽  
Coupling Constant ◽  
Geometric Phases ◽  
Coupled Subsystems ◽  
Two Level Systems ◽  
The Individual

The application of geometric phases into robust control of quantal systems has triggered exploration of the geometric phase for coupled subsystems. Earlier studies have mainly focused on the situation where the external control parameters are in the free Hamiltonian of the subsystems, i.e. the controls exert only on the individual subsystems. Here we consider another circumstance that we can control the coupling geiϕ between the subsystems. By changing only the phase ϕ in the coupling constant, we derive the Berry phase acquired by the system and compare it to the geometric phase acquired by changing the coupling strength g. We find that the asymptotic behavior of the Berry phase depends on the relative Rabi frequency of the two subsystems, and it approaches π when the amplitude of the coupling tends to infinity.

scholarly journals Gravity-Induced Geometric Phases and Entanglement in Spinors and Neutrinos: Gravitational Zeeman Effect

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 160
Author(s):  
Banibrata Mukhopadhyay ◽  
Soumya Kanti Ganguly
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Geometric Phase ◽  
Zeeman Effect ◽  
Relative Strength ◽  
Entangled States ◽  
Neutrino Masses ◽  
Geometric Phases ◽  
Aharonov Bohm ◽  
Gravitational Background

We show Zeeman-like splitting in the energy of spinors propagating in a background gravitational field, analogous to the spinors in an electromagnetic field, otherwise termed the Gravitational Zeeman Effect. These spinors are also found to acquire a geometric phase, in a similar way as they do in the presence of magnetic fields. However, in a gravitational background, the Aharonov-Bohm type effect, in addition to Berry-like phase, arises. Based on this result, we investigate geometric phases acquired by neutrinos propagating in a strong gravitational field. We also explore entanglement of neutrino states due to gravity, which could induce neutrino-antineutrino oscillation in the first place. We show that entangled states also acquire geometric phases which are determined by the relative strength between gravitational field and neutrino masses.

All-optical polarimetric generation of mixed-state single-photon geometric phases

2016 ◽  
Vol 93 (1) ◽  
Author(s):  
D. Barberena ◽  
O. Ortíz ◽  
Y. Yugra ◽  
R. Caballero ◽  
F. De Zela
Keyword(s):  
Mixed State ◽  
Single Photon ◽  
Geometric Phases ◽  
All Optical

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 Mixed State Geometric Phases, Entangled Systems, and Local Unitary Transformations

2003 ◽  
Vol 91 (9) ◽  
Author(s):  
Marie Ericsson ◽  
Arun K. Pati ◽  
Erik Sjöqvist ◽  
Johan Brännlund ◽  
Daniel K. L. Oi
Keyword(s):  
Mixed State ◽  
Geometric Phases ◽  
Unitary Transformations
Sign in / Sign up

Export Citation Format

Share Document