We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schrodinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The NRT non-linear equation admits plane wave-like soluti
ons ($q$-plane waves) compatible with the celebrated de Broglie relations connecting wave number and frequency, respectively, with energy and momentum. The NRT equation, inspired in the $q$-generalized thermostatistical formalism, is characterized by a parameter $q$, and in the limit $q to 1$ reduces to the standard, linear Schrodinger equation. The $q$-Gaussian solutions to the NRT equation investigated here admit as a particular instance the previously known $q$-plane wave solutions. The present work thus extends the range of possible processes yielded by the NRT dynamics that admit an analytical, exact treatment. In the $q to 1$ limit the $q$-Gaussian solutions correspond to the Gaussian wave packet solutions to the free particle linear Schrodinger equation. In the present work we also show that there are other families of nonlinear Schrodinger-like equations, besides the NRT one, exhibiting a dynamics compatible with the de Broglie relations. Remarkably, however, the existence of time dependent Gaussian-like wave packet solutions is a unique feature of the NRT equation not shared by the aforementioned, more general, families of nonlinear evolution equations.
We determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannons or Tsallis entropies in the concomitant variational problem. It is shown that the two variations
lead to equivalent solutions that take different appearances but contain the same information. These solutions are linked by our transformation.
Schrodingers equation (SE) and the information-optimizing principle based on Fishers information measure (FIM) are intimately linked, which entails the existence of a Legendre transform structure underlying the SE. In this comunication we show that t
he existence of such an structure allows, via the virial theorem, for the formulation of a parameter-free ground states SE-ansatz for a rather large family of potentials. The parameter-free nature of the ansatz derives from the structural information it incorporates through its Legendre properties.
It is well known that a suggestive connection links Schrodingers equation (SE) and the information-optimizing principle based on Fishers information measure (FIM). It has been shown that this entails the existence of a Legendre transform structure un
derlying the SE. Such a structure leads to a first order partial differential equation (PDE) for the SEs eigenvalues from which a complete solution for them can be obtained. As an application we deal with the quantum theory of anharmonic oscillators, a long-standing problem that has received intense attention motivated by problems in quantum field theory and molecular physics. By appeal to the Cramer Rao bound we are able to Fisher-infer the particular PDE-solution that yields the eigenvalues without explicitly solving Schrodingers equation. Remarkably enough, and in contrast with standard variational approaches, our present procedure does not involve free fitting parameters.
It is well known that a suggestive relation exists that links Schrodingers equation (SE) to the information-optimizing principle based on Fishers information measure (FIM). The connection entails the existence of a Legendre transform structure underl
ying the SE. Here we show that appeal to this structure leads to a first order differential equation for the SEs eigenvalues that, in certain cases, can be used to obtain the eigenvalues without explicitly solving SE. Complying with the above mentioned equation constitutes a necessary condition to be satisfied by an energy eigenvalue. We show that the general solution is unique.
We discuss some properties of the quantum discord based on the geometric distance advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. {bf 105}, 190502 (2010)], with emphasis on Werner- and MEM-states. We ascertain just how good the measure is in
representing quantum discord. We explore the dependence of quantum discord on the degree of mixedness of the bipartite states, and also its connection with non-locality as measured by the maximum violation of a Bell inequality within the CHSH scenario.
Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total syst
em, on the one hand, and the entropy of the one particle reduced density matrix, on the other one. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Renyis entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Renyis entropic parameter is investigated. The extension of these criteria to systems of $N$ identical fermions is also considered.
The dynamics of the Buck and Sukumar model [B. Buck and C.V. Sukumar, Phys. Lett. A 81 (1981) 132] are investigated using different semi-classical information-theory tools. Interesting aspects of the periodicity inherent to the model are revealed and
somewhat unexpected features are revealed that seem to be related to the classical-quantum transition.
By recourse to i) the Hellmann-Feynman theorem and ii) the Virial one, the information-optimizing principle based on Fishers information measure uncovers a Legendre-transform structure associated with Schrodingers equation, in close analogy with the
structure that lies behind the standard thermodynamical formalism. The present developments provide new evidence for the information theoretical links based on Fishers measure that exist between Schrodingers equation, on the one hand, and thermodynamics/thermostatistics on the other one.
It is well known that a suggestive relation exists that links Schrodingers equation (SE) to the information-optimizing principle based on Fishers information measure (FIM). We explore here an approach that will allow one to infer the optimal FIM comp
atible with a given amount of prior information without explicitly solving first the associated SE. This technique is based on the virial theorem and it provides analytic solutions for the physically relevant FIM, that which is minimal subject to the constraints posed by the prior information.
