Search results for "Geometric"
showing 10 items of 652 documents
The quantum trajectory approach to geometric phase for open systems
2005
The quantum jump method for the calculation of geometric phase is reviewed. This is an operational method to associate a geometric phase to the evolution of a quantum system subjected to decoherence in an open system. The method is general and can be applied to many different physical systems, within the Markovian approximation. As examples, two main source of decoherence are considered: dephasing and spontaneous decay. It is shown that the geometric phase is to very large extent insensitive to the former, i.e. it is independent of the number of jumps determined by the dephasing operator.
Geometry of quantum phase transitions
2020
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric information in the characterisation of quantum phase transitions, we describe recent developments of geometrical approaches based on mixed-state generalisation of the Berry-phase, i.e. the Uhlmann geometric phase, for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs ). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions, whereas i…
Geometric phases and criticality in spin chain systems
2005
A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition. We analytically evaluate the geometric phase that correspond to the ground and excited states of the anisotropic XY model in the presence of a transverse magnetic field when the direction of the anisotropy is adiabatically rotated. Ultra-cold atoms in optical lattices are presented as a possible physical realization.
Scaling of Berry's phase close to the Dicke quantum phase transition
2006
We discuss the thermodynamic and finite size scaling properties of the geometric phase in the adiabatic Dicke model, describing the super-radiant phase transition for an $N$ qubit register coupled to a slow oscillator mode. We show that, in the thermodynamic limit, a non zero Berry phase is obtained only if a path in parameter space is followed that encircles the critical point. Furthermore, we investigate the precursors of this critical behavior for a system with finite size and obtain the leading order in the 1/N expansion of the Berry phase and its critical exponent.
Comment on “Indications of aT=0Quantum Phase Transition inSrTiO3”
1998
A Comment on the Letter by Daniel E. Grupp and Allen M. Goldman, Phys. Rev. Lett. 78, 3511 (1997). The authors of the Letter offer a Reply.
On the rigidity theorem for elliptic genera
2018
We give a detailed proof of the rigidity theorem for elliptic gen- era. Using the Lefschetz fixed point formula we carefully analyze the relation between the characteristic power series defining the elliptic genera and the equivariant elliptic genera. We show that equivariant elliptic genera converge to Jacobi functions which are holomorphic. This implies the rigidity of elliptic genera. Our approach can be easily modified to give a proof of the rigidity theorem for the elliptic genera of level N.
Cone conditions and quasiconformal mappings
1988
Let f be a quasiconformal mapping of the open unit ball B n = {x ∈ R n : | x | < l× in euclidean n-space R n onto a bounded domain D in that space. For dimension n= 2 the literature of geometric function theory abounds in results that correlate distinctive geometric properties of the domain D with special behavior, be it qualitative or quantitative, on the part of f or its inverse. There is a more modest, albeit growing, body of work that attempts to duplicate in dimensions three and above, where far fewer analytical tools are at a researcher’s disposal, some of the successes achieved in the plane along such lines. In this paper we contribute to that higher dimensional theory some observati…
"Table 22" of "Freeze-out radii extracted from three-pion cumulants in pp, p-Pb and Pb-Pb collisions at the LHC"
2014
Exponential radii scaled down by sqrt(pi) and intercept parameters in PbPb collisions versus Nch at low KT3.
"Table 25" of "Freeze-out radii extracted from three-pion cumulants in pp, p-Pb and Pb-Pb collisions at the LHC"
2014
Exponential radii scaled down by sqrt(pi) and intercept parameters in PbPb collisions versus Nch at high KT3.
"Table 20" of "Freeze-out radii extracted from three-pion cumulants in pp, p-Pb and Pb-Pb collisions at the LHC"
2014
Exponential radii scaled down by sqrt(pi) and intercept parameters in pp collisions versus Nch at low KT3.