Detecting the Lee-Yang zeros of a high-spin system by the evolution of probe spin

Recently in paper [Peng et al., Phys. Rev. Lett. 114, 010601 (2015)] the experimental observation of the Lee-Yang zeros of an Ising-type spin-1/2 bath, by measuring the coherence of a probe spin, was reported. We generalize this problem to the case of an arbitrary high-spin bath. Namely, we consider the evolution of a probe arbitrary spin which interacts with bath composed by N arbitrary spins. As a result, the connection between the observed values of the probe spin, such as magnetization and susceptibility, and the Lee-Yang zeros is found. We apply these results to some models, namely, a triangle spin cluster, the Ising model with a long-range interaction and the 1D Ising model with nearest-neighbor interaction. Also we propose the implementation of these models on real physical systems.Comment: 13 pages, 6 figure

Quantum brachistochrone problem for spin-1 in a magnetic field

We study quantum brachistochrone problem for the spin-1 system in a magnetic field of a constant absolute value. Such system gives us a possibility to examine in detail the statement of papers [A. Carlini {\it et al.}, Phys. Rev. Lett. {\bf 96}, 060503 (2006), D. C. Brody, D. W. Hook, J. Phys. A {\bf 39}, L167, (2006)] that {\it the state vectors realizing the evolution with the minimal time of passage evolve along the subspace spanned by the initial and final state vectors.} Using explicit example we show the existence of quantum brachistochrone with minimal possible time, but the state vector of which, during the evolution {\em leaves} the subspace spanned by the initial and final state vectors. This is the result of the choice of more constrained Hamiltonian then assumed in the general quantum brachistochrone problem, but what is worth noting, despite that such evolution is more complicated it is still time optimal. This might be important for experiment, where general Hamiltonian with the all allowed parameters is difficult to implement, but constrained one depending on magnetic field can be realized. However for pre-constrained Hamiltonian not all final states are accessible. Present result does not contradict general statement of the quantum brachistochrone problem, but gives new insight how time optimal passage can be realized.Comment: 7 pages, no figure

Time correlation functions and Fisher zeros for q-deformed Bose gas

The time-dependent correlation functions of q-deformed Bose gas are studied. We find relation of zeros of the correlation functions with the Fisher zeros of partition function of the system. Complex temperature appears as a result of q-deformation and evolution of correlation function. A particular case of q-deformed Bose particles on two levels is examined and zeros of correlation functions and Fisher zeros of partition function are analyzed

Maths-type q-deformed coherent states for q > 1

Maths-type q-deformed coherent states with $q > 1$ allow a resolution of unity in the form of an ordinary integral. They are sub-Poissonian and squeezed. They may be associated with a harmonic oscillator with minimal uncertainties in both position and momentum and are intelligent coherent states for the corresponding deformed Heisenberg algebra.Comment: LaTeX2e, 15 pages + 3 eps figures, figures replace