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Ramandeep S. Johal

Publications and source records attributed to Ramandeep S. Johal.

67 records · Page 4Linked to original sources
arXiv2002

On the correct entropic form for systems with power-law behaviour: the case of dissipative maps

Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar power-law distributions. In this paper, we address the question whether the Renyi entropy is equally suitable to describe those systems with power-law behaviour, where the use of the Tsallis entropy is relevant. We discuss a specific class of dynamical systems, namely, one dimensional dissipative maps at chaos threshold and make our study from two aspects: i) power-law sensitivity to the initial conditions and the rate of entropy increase, ii) generalized bit cumulants. We present evidence that the Tsallis entropy is the more appropriate entropic form for such studies as opposed to Renyi form.

cond-mat.stat-mech↗
arXiv2002

On matrix elements of phase-angular momentum commutator in Hilbert space of arbitrary dimensions

We discuss correspondence between the predictions of quantum theories for rotation angle formulated in infinite and finite dimensional Hilbert spaces, taking as example, the calculation of matrix elements of phase-angular momentum commutator. A new derivation of the matrix elements is presented in infinite space, making use of a unitary transformation that maps from the state space of periodic functions to non-periodic functions, over which the spectrum of angular momentum operator is in general, fractional. The approach can be applied to finite dimensional Hilbert space also, for which identical matrix elements are obtained.

quant-ph↗
arXiv2001

Dynamics with unitary phase operator:implications for Wigner's problem

We show that for general deformations of SU(2) algebra, the dynamics in terms of ladder operators is preserved. This is done for a system of precessing magnetic dipole in magnetic field, using the unitary phase operator which arises in the polar decomposition of SU(2) operators. It is pointed out that there is a single phase operator dynamics underlying the dynamics of usual and deformed ladder operators.

quant-ph↗
arXiv2000

q-deformed dynamics and Josephson junction

We define a generalized rate equation for an observable in quantum mechanics, that involves a parameter q and whose limit $q\to 1$ gives the standard Heisenberg equation. The generalized rate equation is used to study dynamics of current biased Josephson junction. It is observed that this toy model incorporates diffraction like effects in the critical current. Physical interpretation for q is provided which is also shown to be q-deformation parameter.

quant-ph↗
arXiv2000

Phase shift operator and cyclic evolution in finite dimensional Hilbert space

We address the problem of phase shift operator acting as time evolution operator in Pegg-Barnett formalism. It is argued that standard shift operator is inconsistent with the behaviour of the state vector under cyclic evolution. We consider a generally deformed oscillator algebra at q-root of unity, as it yields the same Pegg-Barnett operator and show that shift operator meets our requirement.

quant-ph↗
arXiv1999

Nonextensive thermodynamic formalism for chaotic dynamical systems

A nonextensive thermostatic approach to chaotic dynamical systems is developed by expressing generalized Tsallis distribution as escort distribution. We explicitly show the thermodynamic limit and also derive the Legendre Transform structure. As an application, bit variance is calculated for ergodic logistic map. Consistency of the formalism demands a relation between box size ($ε$) and degree of nonextensivity, given as $(1-q)\sim -1/{\rm ln} ε$. This relation is numerically verified for the case of bit variance as well as using basic definition of Tsallis entropy.

cond-mat.stat-mech↗
arXiv1999

Inferring degree of nonextensivity for generalized entropies

The purpose of this note is to argue that degree of nonextensivity as given by Tsallis distribution obtained from maximum entropy principle has a different origin than nonextensivity inferred from pseudo-additive property of Tsallis entropy.

cond-mat.stat-mech↗
arXiv1998

Statistical Distance For Chaotic Maps

The purpose of this letter is to define a distance on the underlying phase space of a chaotic map, based on natural invariant density of the map. It is observed that for logistic map this distance is equivalent to Wootters' statistical distance. This distance becomes the Euclidean distance for a map with constant invariant density.

chao-dyn↗
arXiv1998

q-Calculus Framework For Entropy In Multifractal Distributions

The connection between Tsallis entropy for a multifractal distribution and Jackson's $q$-derivative is established. Based on this derivation and definition of a homogeneous function, a $q$-analogue of Shannon's entropy is discussed. $q$-additivity of this entropy is shown. We also define $q$-analogue of Kullback relative entropy. The implications of lattice structure beneath $q$-calculus are highlighted in the context of $q$-entropy.

cond-mat.stat-mech↗
arXiv1997

Is the Deformation Parameter in q-Rotor Model Really Phenomenological ?

We cast the $q$-rotor in the framework of Barnett-Pegg theory for rotation angle, whose underlying algebra is $SU_q(2)$. A new method to fix the deformation parameter from the theory is suggested. We test our ideas by fitting rotational spectra in deformed even-even and superdeformed nuclei. The results are in good agreement with the previous phenomenological applications of $q$-rotor model.

quant-ph↗
arXiv1997

Angular Velocity Operator and Barnett-Pegg Formalism

We define a new operator within Barnett-Pegg formalism for phase angle. The physical predictions for this operator correspond to those expected of an angular velocity operator. Examples studied are particle on a circle with and without magnetic field and quantum harmonic oscillator.

quant-ph↗