An approach featuring s-parametrized quasiprobability distribution functions is developed for sit... more An approach featuring s-parametrized quasiprobability distribution functions is developed for situations where a circular topology is observed. For such an approach a suitable set of coherent states must be introduced in appropriate fashion. The importance of phase space quasiprobability distribution functions in the description of different physical systems can hardly be overestimated in literature. Apart from its own theoretical interest [1], they play a key role in quantum optics [2], give an appropriate approach to decoherence [3], insights on semi classical methods and alternative approaches for dynamics of quantum systems [4]. Quasiprobability distribution functions are defined on quantum phase spaces. A quantum phase space formalism generally is based on a mapping scheme which enables one to relate operators and functions defined on such phase space [5, 6]. In this kind of approach, the quasiprobability distributions are the functions associated with the density operator. Mea...
Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent tw... more Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent two important results derived of various approaches related to quantum gravity and black hole physics near the well-known Planck scale. The discreteness of space suggests, in particular, that all measurable lengths are quantized in units of a fundamental scale (in this case, the Planck length). Here, we propose a self-consistent theoretical framework for an important class of physical systems characterized by a finite space of states, and show that such a framework enlarges previous knowledge about generalized uncertainty principles, as topological effects in finite-dimensional discrete phase spaces come into play. Besides, we also investigate under what circumstances the generalized uncertainty principle (GUP) works out well and its inherent limitations.
This article presents a squeezing transformation for quantum systems associated to finite vector ... more This article presents a squeezing transformation for quantum systems associated to finite vector spaces. The physical idea of squeezing here is taken from the action of the usual squeezing operator over wave functions defined on a real line, that is, a transformation capable to diminish (or enhance) the mean square deviation of a centered distribution. As it is discussed, the definition of such an operator on finite dimensional vector spaces is not a trivial matter, but, on the other hand, has obvious connections with problems such as spin squeezing and (finite) quantum state reproduction.
In this work we will advance farther along a line previously developed concerning our proposal of... more In this work we will advance farther along a line previously developed concerning our proposal of a time interval operator, on finite dimensional spaces. The time interval operator is Hermitian, and its eigenvalues are time values with a precise and interesting role on the dynamics. With the help of the Discrete Phase Space Formalism (DPSF) previously developed, we show that the time interval operator is the complementary pair of the Hamiltonian. From that, a simple system is proposed as a quantum clock. The only restriction is that our results do not apply to all possible Hamiltonians.
ABSTRACT In recent years, an approach to discrete quantum phase spaces which comprehends all the ... more ABSTRACT In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber–Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism. Keywordsfinite-dimensional quantum systems–coherent states–Wigner function–Husimi function–Glauber–Sudarshan distribution
Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent tw... more Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent two important results derived of various approaches related to quantum gravity and black hole physics near the well-known Planck scale. The discreteness of space suggests, in particular, that all measurable lengths are quantized in units of a fundamental scale (in this case, the Planck length). Here, we propose a self-consistent theoretical framework for an important class of physical systems characterized by a finite space of states, and show that such a framework enlarges previous knowledge about generalized uncertainty principles, as topological effects in finite-dimensional discrete phase spaces come into play. Besides, we also investigate under what circumstances the generalized uncertainty principle (GUP) works out well and its inherent limitations.
Journal of Physics A: Mathematical and General, 2000
ABSTRACT The discrete phase space approach to quantum mechanics of degrees of freedom without cla... more ABSTRACT The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wigner function is written for some chosen states associated to discrete angle and angular momentum variables, and the time evolution is numerically calculated using the discrete von Neumann-Liouville equation. Direct evidences in the time evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU (2)-based semiclassical continuous approach to the Lipkin model is also presented.
Journal of Physics A: Mathematical and General, 2000
The main aspects of a discrete phase space formalism are presented and the discrete dynamical bra... more The main aspects of a discrete phase space formalism are presented and the discrete dynamical bracket, suitable for the description of time evolution in finite-dimensional spaces, is discussed. A set of operator bases is defined in such a way that the Weyl-Wigner formalism is shown to be obtained as a limiting case. In the same form, the Moyal bracket is shown to be the limiting case of the discrete dynamical bracket. The dynamics in quantum discrete phase spaces is shown not to be attained from discretization of the continuous case.
An approach featuring s-parametrized quasiprobability distribution functions is developed for sit... more An approach featuring s-parametrized quasiprobability distribution functions is developed for situations where a circular topology is observed. For such an approach a suitable set of coherent states must be introduced in appropriate fashion. The importance of phase space quasiprobability distribution functions in the description of different physical systems can hardly be overestimated in literature. Apart from its own theoretical interest [1], they play a key role in quantum optics [2], give an appropriate approach to decoherence [3], insights on semi classical methods and alternative approaches for dynamics of quantum systems [4]. Quasiprobability distribution functions are defined on quantum phase spaces. A quantum phase space formalism generally is based on a mapping scheme which enables one to relate operators and functions defined on such phase space [5, 6]. In this kind of approach, the quasiprobability distributions are the functions associated with the density operator. Mea...
Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent tw... more Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent two important results derived of various approaches related to quantum gravity and black hole physics near the well-known Planck scale. The discreteness of space suggests, in particular, that all measurable lengths are quantized in units of a fundamental scale (in this case, the Planck length). Here, we propose a self-consistent theoretical framework for an important class of physical systems characterized by a finite space of states, and show that such a framework enlarges previous knowledge about generalized uncertainty principles, as topological effects in finite-dimensional discrete phase spaces come into play. Besides, we also investigate under what circumstances the generalized uncertainty principle (GUP) works out well and its inherent limitations.
This article presents a squeezing transformation for quantum systems associated to finite vector ... more This article presents a squeezing transformation for quantum systems associated to finite vector spaces. The physical idea of squeezing here is taken from the action of the usual squeezing operator over wave functions defined on a real line, that is, a transformation capable to diminish (or enhance) the mean square deviation of a centered distribution. As it is discussed, the definition of such an operator on finite dimensional vector spaces is not a trivial matter, but, on the other hand, has obvious connections with problems such as spin squeezing and (finite) quantum state reproduction.
In this work we will advance farther along a line previously developed concerning our proposal of... more In this work we will advance farther along a line previously developed concerning our proposal of a time interval operator, on finite dimensional spaces. The time interval operator is Hermitian, and its eigenvalues are time values with a precise and interesting role on the dynamics. With the help of the Discrete Phase Space Formalism (DPSF) previously developed, we show that the time interval operator is the complementary pair of the Hamiltonian. From that, a simple system is proposed as a quantum clock. The only restriction is that our results do not apply to all possible Hamiltonians.
ABSTRACT In recent years, an approach to discrete quantum phase spaces which comprehends all the ... more ABSTRACT In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber–Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism. Keywordsfinite-dimensional quantum systems–coherent states–Wigner function–Husimi function–Glauber–Sudarshan distribution
Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent tw... more Generalized uncertainty principle and breakdown of the spacetime continuum certainly represent two important results derived of various approaches related to quantum gravity and black hole physics near the well-known Planck scale. The discreteness of space suggests, in particular, that all measurable lengths are quantized in units of a fundamental scale (in this case, the Planck length). Here, we propose a self-consistent theoretical framework for an important class of physical systems characterized by a finite space of states, and show that such a framework enlarges previous knowledge about generalized uncertainty principles, as topological effects in finite-dimensional discrete phase spaces come into play. Besides, we also investigate under what circumstances the generalized uncertainty principle (GUP) works out well and its inherent limitations.
Journal of Physics A: Mathematical and General, 2000
ABSTRACT The discrete phase space approach to quantum mechanics of degrees of freedom without cla... more ABSTRACT The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wigner function is written for some chosen states associated to discrete angle and angular momentum variables, and the time evolution is numerically calculated using the discrete von Neumann-Liouville equation. Direct evidences in the time evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with a SU (2)-based semiclassical continuous approach to the Lipkin model is also presented.
Journal of Physics A: Mathematical and General, 2000
The main aspects of a discrete phase space formalism are presented and the discrete dynamical bra... more The main aspects of a discrete phase space formalism are presented and the discrete dynamical bracket, suitable for the description of time evolution in finite-dimensional spaces, is discussed. A set of operator bases is defined in such a way that the Weyl-Wigner formalism is shown to be obtained as a limiting case. In the same form, the Moyal bracket is shown to be the limiting case of the discrete dynamical bracket. The dynamics in quantum discrete phase spaces is shown not to be attained from discretization of the continuous case.
Uploads
Papers by Maurizio Ruzzi