scholarly journals Geometric phase for mixed states: a differential geometric approach

2004 ◽  
Vol 35 (3) ◽  
pp. 413-423 ◽  
Author(s):  
S. Chaturvedi ◽  
E. Ercolessi ◽  
G. Marmo ◽  
G. Morandi ◽  
N. Mukunda ◽  
...  
Keyword(s):  
Geometric Phase ◽  
Geometric Approach ◽  
Mixed States

scholarly journals Geometric approach to non-relativistic quantum dynamics of mixed states

2013 ◽  
Vol 54 (5) ◽  
pp. 052108 ◽  
Author(s):  
Vicent Gimeno ◽  
Jose M. Sotoca
Keyword(s):  
Quantum Dynamics ◽  
Relativistic Quantum ◽  
Geometric Approach ◽  
Mixed States

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.

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.

Geometric phase of mixed states for three-level open systems

2010 ◽  
Vol 82 (6) ◽  
Author(s):  
Yanyan Jiang ◽  
Y. H. Ji ◽  
Hualan Xu ◽  
Li-yun Hu ◽  
Z. S. Wang ◽  
...  
Keyword(s):  
Geometric Phase ◽  
Open Systems ◽  
Mixed States

GEOMETRIC PHASES FOR MIXED STATES DURING UNITARY AND NON-UNITARY EVOLUTIONS

2003 ◽  
Vol 01 (01) ◽  
pp. 135-152 ◽  
Author(s):  
ARUN K. PATI
Keyword(s):  
Geometric Phase ◽  
Parallel Transport ◽  
Quantum Systems ◽  
Mixed States ◽  
Completely Positive Maps ◽  
Initial State ◽  
Unitary Evolution ◽  
Completely Positive ◽  
Quantum Operations ◽  
Positive Maps

Mixed states typically arise when quantum systems interact with the outside world. Evolution of open quantum systems in general are described by quantum operations which are represented by completely positive maps. We elucidate the notion of geometric phase for a quantum system described by a mixed state undergoing unitary evolution and non-unitary evolutions. We discuss parallel transport condition for mixed states both in the case of unitary maps and completely positive maps. We find that the relative phase shift of a system not only depends on the state of the system, but also depends on the initial state of the ancilla with which it might have interacted in the past. The geometric phase change during a sequence of quantum operations is shown to be non-additive in nature. This property can attribute a "memory" to a quantum channel. We explore these ideas and illustrate them with simple examples.

Geometric phase for mixed states

Laser Physics ◽  
2006 ◽  
Vol 16 (2) ◽  
pp. 398-401
Author(s):  
L. C. Kwek ◽  
D. M. Tong ◽  
J. L. Chen ◽  
J. F. Du ◽  
K. W. Choo ◽  
...  
Keyword(s):  
Geometric Phase ◽  
Mixed States

scholarly journals Measurement of Geometric Phase for Mixed States Using Single Photon Interferometry

2005 ◽  
Vol 94 (5) ◽  
Author(s):  
Marie Ericsson ◽  
Daryl Achilles ◽  
Julio T. Barreiro ◽  
David Branning ◽  
Nicholas A. Peters ◽  
...  
Keyword(s):  
Geometric Phase ◽  
Single Photon ◽  
Mixed States
Sign in / Sign up

Export Citation Format

Share Document