1,574 research outputs found
Noncyclic and nonadiabatic geometric phase for counting statistics
We propose a general framework of the geometric-phase interpretation for
counting statistics. Counting statistics is a scheme to count the number of
specific transitions in a stochastic process. The cumulant generating function
for the counting statistics can be interpreted as a `phase', and it is
generally divided into two parts: the dynamical phase and a remaining one. It
has already been shown that for cyclic evolution the remaining phase
corresponds to a geometric phase, such as the Berry phase or Aharonov-Anandan
phase. We here show that the remaining phase also has an interpretation as a
geometric phase even in noncyclic and nonadiabatic evolution.Comment: 12 pages, 1 figur
CHARACTERIZATION OF THE SUPPORT OF THE MIXED STRATEGY PRICE EQUILIBRIA IN OLIGOPOLIES WITH HETEROGENEOUS CONSUMERS
This paper revisits the theory of oligopoly pricing and shows that for a large class of demand and cost functions, a mixed strategy equilibrium necessarily implies that each firm’s equilibrium strategy is a discrete distribution over a finite number of prices.
Qualitative Analysis of the Classical and Quantum Manakov Top
Qualitative features of the Manakov top are discussed for the classical and
quantum versions of the problem. Energy-momentum diagram for this integrable
classical problem and quantum joint spectrum of two commuting observables for
associated quantum problem are analyzed. It is demonstrated that the evolution
of the specially chosen quantum cell through the joint quantum spectrum can be
defined for paths which cross singular strata. The corresponding quantum
monodromy transformation is introduced.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on
Integrable Systems and Related Topics, published in SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
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