Applications of algebras in physics are related to the connection of measurable observables to re... more Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we have not enough primitive elements that allow for a privileged set of generators and all basic sets are equivalent. In this paper we discuss how the Drinfeld double structure underlying every simple Lie bialgebra characterizes uniquely a particular basis without any freedom, completing the Cartan program on simple algebras. By means of a perturbative construction, a distinguished deformed basis (we call it the analytical basis) is obtained for every quantum group as the analytical prolongation of the above defined Lie basis of the corresponding Lie bialgebra. It turns out that the whole construc...
ABSTRACT In a recent paper [Phys. Rev. Lett. 66, 2056 (1991)] the authors have shown how the two ... more ABSTRACT In a recent paper [Phys. Rev. Lett. 66, 2056 (1991)] the authors have shown how the two concepts of quantum groups and squeezing can be bridged in the simple setting provided by a set of states which are a modified version of the states introduced by L. C. Biedenharn and A. J. McFarlane [J. Phys. A, Math. Gen. 22, L873–L878 (1989; Zbl 0708.17015), ibid. 22, 4581-4588 (1989; Zbl 0722.17009)]. They conjecture that the notion of quantum group coherent state is in general the natural candidate to describe squeezed quantum states of matter.
A quantitative analysis of the process of condensation of bosons both in harmonic traps and in ga... more A quantitative analysis of the process of condensation of bosons both in harmonic traps and in gases is made resorting to two ingredients only: Bose classical distribution and spectral discretness. It is shown that in order to take properly into account statistical correlations, temperature must be defined from first principles, based on Shannon entropy, and turns out to be equal to $\beta^{-1}$ only for $T > T_c$ where the usual results are recovered. Below $T_c$ a new critical temperature $T_d$ is found, where the specific heat exhibits a sharp spike, similar to the $\lambda$-peak of superfluidity.
The Energy Citations Database (ECD) provides access to historical and current research (1948 to t... more The Energy Citations Database (ECD) provides access to historical and current research (1948 to the present) from the Department of Energy (DOE) and predecessor agencies.
The conventional squeezed states of quantum optics, which can be thought of as generalized cohere... more The conventional squeezed states of quantum optics, which can be thought of as generalized coherent states for the algebra SU(1,1), are dynamically generated by single-mode hamiltonians characterized by two-photon process interactions. By the explicit construction of a (highly non-linear) faithful realization of the group [Formula: see text] of automorphisms of SU(1,1), such hamiltonians are shown to be equivalent — up just to elements of [Formula: see text] — to that describing quantum mechanically a damped oscillator.
Applications of algebras in physics are related to the connection of measurable observables to re... more Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we have not enough primitive elements that allow for a privileged set of generators and all basic sets are equivalent. In this paper we discuss how the Drinfeld double structure underlying every simple Lie bialgebra characterizes uniquely a particular basis without any freedom, completing the Cartan program on simple algebras. By means of a perturbative construction, a distinguished deformed basis (we call it the analytical basis) is obtained for every quantum group as the analytical prolongation of the above defined Lie basis of the corresponding Lie bialgebra. It turns out that the whole construc...
ABSTRACT In a recent paper [Phys. Rev. Lett. 66, 2056 (1991)] the authors have shown how the two ... more ABSTRACT In a recent paper [Phys. Rev. Lett. 66, 2056 (1991)] the authors have shown how the two concepts of quantum groups and squeezing can be bridged in the simple setting provided by a set of states which are a modified version of the states introduced by L. C. Biedenharn and A. J. McFarlane [J. Phys. A, Math. Gen. 22, L873–L878 (1989; Zbl 0708.17015), ibid. 22, 4581-4588 (1989; Zbl 0722.17009)]. They conjecture that the notion of quantum group coherent state is in general the natural candidate to describe squeezed quantum states of matter.
A quantitative analysis of the process of condensation of bosons both in harmonic traps and in ga... more A quantitative analysis of the process of condensation of bosons both in harmonic traps and in gases is made resorting to two ingredients only: Bose classical distribution and spectral discretness. It is shown that in order to take properly into account statistical correlations, temperature must be defined from first principles, based on Shannon entropy, and turns out to be equal to $\beta^{-1}$ only for $T > T_c$ where the usual results are recovered. Below $T_c$ a new critical temperature $T_d$ is found, where the specific heat exhibits a sharp spike, similar to the $\lambda$-peak of superfluidity.
The Energy Citations Database (ECD) provides access to historical and current research (1948 to t... more The Energy Citations Database (ECD) provides access to historical and current research (1948 to the present) from the Department of Energy (DOE) and predecessor agencies.
The conventional squeezed states of quantum optics, which can be thought of as generalized cohere... more The conventional squeezed states of quantum optics, which can be thought of as generalized coherent states for the algebra SU(1,1), are dynamically generated by single-mode hamiltonians characterized by two-photon process interactions. By the explicit construction of a (highly non-linear) faithful realization of the group [Formula: see text] of automorphisms of SU(1,1), such hamiltonians are shown to be equivalent — up just to elements of [Formula: see text] — to that describing quantum mechanically a damped oscillator.
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