The Caldeira-Leggett Hamiltonian describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature physics, and has... more
The Caldeira-Leggett Hamiltonian describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature physics, and has applications to superconductors, quantum computing, and macroscopic quantum tunneling. The similarities between the Caldeira-Leggett model and the linearized Vlasov-Poisson equation are analyzed, and it is shown that the damping in the Caldeira-Leggett model is analogous to that of Landau damping in plasmas (Landau, 1946 [1]). An invertible linear transformation (Morrison and Pfirsch, 1992 [18]; Morrison, 2000 [19]) is presented that converts solutions of the Caldeira-Leggett model into solutions of the linearized Vlasov-Poisson system.
Radiating dipoles in photonic crystals. Kurt Busch 1,2 , Nipun Vats 1 , Sajeev John 1 , and Barry C. Sanders 3 1 Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7 2 Institut ...
We discuss an experiment for determining the heat capacities of various solids based on a calorimetric approach where the solid vaporizes a measurable mass of liquid nitrogen. We demonstrate our technique for copper and aluminum, and... more
We discuss an experiment for determining the heat capacities of various solids based on a calorimetric approach where the solid vaporizes a measurable mass of liquid nitrogen. We demonstrate our technique for copper and aluminum, and compare our data with Einstein's model of independent harmonic oscillators and the more accurate Debye model. We also illustrate an interesting material property, the Verwey transition in magnetite.
In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested Schrödinger quantum mechanics. The... more
In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested Schrödinger quantum mechanics. The kinematical cornerstone of our framework is the so-called polymer representation of the Heisenberg Weyl (HW) algebra, which is the starting point of the construction.
We discuss a model of repeated measurements of position in a quantum system which is monitored for a finite amount of time with a finite instrumental error. In this framework we recover the optimum monitoring of a harmonic oscillator... more
We discuss a model of repeated measurements of position in a quantum system which is monitored for a finite amount of time with a finite instrumental error. In this framework we recover the optimum monitoring of a harmonic oscillator proposed in the case of an instantaneous collapse of the wavefunction into an infinite-accuracy measurement result. We also establish numerically the existence of an optimal measurement strategy in the case of a nonlinear system. This optimal strategy is completely defined by the spectral properties of the nonlinear system.
We propose a procedure based on symplectic tomography for reconstructing the unknown parameters of a convolutionless non-Markovian Gaussian noisy evolution. Whenever the time-dependent master equation coefficients are given as a function... more
We propose a procedure based on symplectic tomography for reconstructing the unknown parameters of a convolutionless non-Markovian Gaussian noisy evolution. Whenever the time-dependent master equation coefficients are given as a function of some unknown time-independent parameters, we show that these parameters can be reconstructed by means of a finite number of tomograms. Two different approaches towards reconstruction, integral and differential, are presented and applied to a benchmark model made of a harmonic oscillator coupled to a bosonic bath. For this model the number of tomograms needed to retrieve the unknown parameters is explicitly computed.
The Lagrangian and the Generalized Linear Momentum are given in terms of a constant of motion for a one-dimensional autonomous system. The possibility of having an explicit Hamiltonian expression is also analyzed. The approach is applied... more
The Lagrangian and the Generalized Linear Momentum are given in terms of a constant of motion for a one-dimensional autonomous system. The possibility of having an explicit Hamiltonian expression is also analyzed. The approach is applied to some dissipative systems. Copyright {copyright} 1996 Academic Press, Inc.
The equivalence between the q-deformed harmonic oscillator and a specific anharmonic oscillator model, by which some new insight into the problem of the physical meaning of the parameter q can be attained, are discussed.
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck... more
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle and a simple cosmological model.
The infrared spectrum of the ammonia water complex has been recorded from 10 to 4000 cm for complexes trapped in neon and krypton matrices. Spectra have been observed for NH or ND complexed with HO, HDO, or DO. The observed intramolecular... more
The infrared spectrum of the ammonia water complex has been recorded from 10 to 4000 cm for complexes trapped in neon and krypton matrices. Spectra have been observed for NH or ND complexed with HO, HDO, or DO. The observed intramolecular fundamentals are ...
This paper studies a model of cooperative behavior in a multi-robot system that consists of N mobile robots. It is assumed that the robots correspond to diffusing particles, and interact to each other as the theory of Brownian motion... more
This paper studies a model of cooperative behavior in a multi-robot system that consists of N mobile robots. It is assumed that the robots correspond to diffusing particles, and interact to each other as the theory of Brownian motion predicts. Brownian motion is the analogous of the quantum harmonic oscillator (Q.H.O.), i.e. of Schrodinger's equation under harmonic (parabolic) potential. It is shown that the motion of the robots can be described by Langevin's equation which is a stochastic linear differential equation. It is proved that Langevin's equation is a generalization of conventional gradient algorithms. Therefore the kinematic models of mobile robots which follow conventional gradient algorithms can be considered as a subcase of the kinematic models which are derived from the diffusion analogous of the Q.H.O model.
The Lagrangian and the Generalized Linear Momentum are given in terms of a constant of motion for a one-dimensional autonomous system. The possibility of having an explicit Hamiltonian expression is also analyzed. The approach is applied... more
The Lagrangian and the Generalized Linear Momentum are given in terms of a constant of motion for a one-dimensional autonomous system. The possibility of having an explicit Hamiltonian expression is also analyzed. The approach is applied to some dissipative systems. Copyright {copyright} 1996 Academic Press, Inc.
Volterra series provides a strong platform for non-linear analysis and higher order frequency response functions. However, limited convergence is an inherent difficulty associated with the series and needs to be addressed rigorously,... more
Volterra series provides a strong platform for non-linear analysis and higher order frequency response functions. However, limited convergence is an inherent difficulty associated with the series and needs to be addressed rigorously, prior to its application to a physical ...
Discharge and recharge of the warm water volume (WWV) above the 20°C isotherm in an equatorial Pacific Ocean box extending across the Pacific from 156°E to the eastern ocean boundary between latitudes 5°S and 5°N are key variables in ENSO... more
Discharge and recharge of the warm water volume (WWV) above the 20°C isotherm in an equatorial Pacific Ocean box extending across the Pacific from 156°E to the eastern ocean boundary between latitudes 5°S and 5°N are key variables in ENSO dynamics. A formula linking WWV anomalies, zonally integrated wind stress curl anomalies along the northern and southern edges of the box, and flow into the western end of the box is derived and tested using monthly data since 1993. Consistent with previous work, a WWV balance can only be achieved if the 20°C isotherm surface is not a material surface; that is, warm water can pass through it. For example, during El Niño, part of the WWV anomaly entering the box is cooled so that it is less than 20°C and therefore passes out of the bottom of the box, the 20°C isotherm surface. The observations suggest that the anomalous volume passing through the 20°C isotherm is approximately the same as T ′W, the anomalous WWV entering the western end of the box. ...
