Collective performance of a finite-time quantum Otto cycle

We study the finite-time effects in a quantum Otto cycle where a collective spin system is used as the working fluid. Starting from a simple one-qubit system we analyze the transition to the limit cycle in the case of a finite-time thermalization. If the system consists of a large sample of independent qubits interacting coherently with the heat bath, the superradiant equilibration is observed. We show that this phenomenon can boost the power of the engine. Mutual interaction of qubits in the working fluid is modeled by the Lipkin-Meshkov-Glick Hamiltonian. We demonstrate that in this case the quantum phase transitions for the ground and excited states may have a strong negative effect on the performance of the machine. Reversely, by analyzing the work output we can distinguish between the operational regimes with and without a phase transition.Comment: 13 pages, 11 figure

Thermodynamic Analogy for Structural Phase Transitions

We investigate the relationship between ground-state (zero-temperature) quantum phase transitions in systems with variable Hamiltonian parameters and classical (temperature-driven) phase transitions in standard thermodynamics. An analogy is found between (i) phase-transitional distributions of the ground-state related branch points of quantum Hamiltonians in the complex parameter plane and (ii) distributions of zeros of classical partition functions in complex temperatures. Our approach properly describes the first- and second-order quantum phase transitions in the interacting boson model and can be generalized to finite temperatures.Comment: to be published by AIP in Proc. of the Workshop "Nuclei and Mesoscopic Physics" (Michigan State Univ., Oct 2004); 10 pages, 3 figure

Parameter symmetries of quantum many-body systems

We analyze the occurrence of dynamically equivalent Hamiltonians in the parameter space of general many-body interactions for quantum systems, particularly those that conserve the total number of particles. As an illustration of the general framework, the appearance of parameter symmetries in the interacting boson model-1 and their absence in the Ginocchio SO(8) fermionic model are discussed.Comment: 8 pages, REVTeX, no figur

Phase transitions in the sdgsdg interacting boson model

A geometric analysis of the $sdg$ interacting boson model is performed. A coherent-state is used in terms of three types of deformation: axial quadrupole ($\beta_2$), axial hexadecapole ($\beta_4$) and triaxial ($\gamma_2$). The phase-transitional structure is established for a schematic $sdg$ hamiltonian which is intermediate between four dynamical symmetries of U(15), namely the spherical ${\rm U}(5)\otimes{\rm U}(9)$, the (prolate and oblate) deformed ${\rm SU}_\pm(3)$ and the $\gamma_2$-soft SO(15) limits. For realistic choices of the hamiltonian parameters the resulting phase diagram has properties close to what is obtained in the $sd$ version of the model and, in particular, no transition towards a stable triaxial shape is found.Comment: 19 pages, 5 figures, submitted to J. Phys.