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Pulak Ranjan Giri

Publications and source records attributed to Pulak Ranjan Giri.

48 records · Page 3Linked to original sources
arXiv2007

Inequivalent quantization in the field of a ferromagnetic wire

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann's method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ\in\mathbb{R}({mod}2π). There exists a single bound state for the coupling constant η^2\in[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η^2< 0, which supports bound state making the problem re-normalizable.

cond-mat.mtrl-sci↗
arXiv2007

Self-Adjointness of Generalized MIC-Kepler System

We have studied the self-adjointness of generalized MIC-Kepler Hamiltonian, obtained from the formally self-adjoint generalized MIC-Kepler Hamiltonian. We have shown that for \tilde l=0, the system admits a 1-parameter family of self-adjoint extensions and for \tilde l \neq 0 but \tilde l <{1/2}, it has also a 1-parameter family of self-adjoint extensions.

hep-th↗
arXiv2007

Supersymmetric quantum mechanical generalized MIC-Kepler system

We construct supersymmetric (SUSY) generalized MIC-Kepler system and show that the systems with half integral Dirac quantization condition μ= \pm{1/2}, \pm{3/2}, \pm{5/2},..... belong to a SUSY family (hierarchy of Hamiltonian) with same spectrum between the respective partner Hamiltonians except for the ground state. Similarly, the systems with integral Dirac quantization condition μ=\pm 1,\pm 2, \pm 3,...... belong to another family. We show that, it is necessary to introduce additional potential to MIC-Kepler system in order to unify the two families into one. We also reproduce the results of the (super-symmetric) Hydrogenic problem in our study.

hep-th↗
arXiv2007

Quantization of neutron in Earth's gravity

Gravity is the weakest of all four known forces in the universe. Quantum states of an elementary particle due to such a weak field is certainly very shallow and would therefore be an experimental challenge to detect. Recently an experimental attempt was made by V. V. Nesvizhevsky et al., Nature 415, 297 (2002), to measure the quantum states of a neutron, which shows that ground state and few excited states are \sim 10^{-12}eV. We show that the energy of the ground state of a neutron confined above Earth's surface should be \sim 10^{-37}eV. The experimentally observed energy levels are 10^{25} times deeper than the actual energy levels it should be and thus certainly not due to gravitational effect of Earth. Therefore the correct interpretation for the painstaking experimental results of Ref. \cite{nes1} is due to the confinement potential of a one dimensional box of length L \sim 50μm, generated from the experimental setup as commented before \cite{hansoon}. Our results thus creates a new challenge to the experimentalist to resolve the shallow energy levels of the neutron in Earth's gravitational field in future.

hep-th↗
arXiv2007

Hidden scale in quantum mechanics

We show that the intriguing localization of a free particle wave-packet is possible due to a hidden scale present in the system. Self-adjoint extensions (SAE) is responsible for introducing this scale in quantum mechanical models through the nontrivial boundary conditions. We discuss a couple of classically scale invariant free particle systems to illustrate the issue. In this context it has been shown that a free quantum particle moving on a full line may have localized wave-packet around the origin. As a generalization, it has also been shown that particles moving on a portion of a plane or on a portion of a three dimensional space can have unusual localized wave-packet.

hep-th↗
arXiv2007

Dipole binding in a cosmic string background due to quantum anomalies

We propose quantum dynamics for the dipole moving in cosmic string background and show that the classical scale symmetry of a particle moving in cosmic string background is still restored even in the presence of dipole moment of the particle. However, we show that the classical scale symmetry is broken due to inequivalent quantization of the the non-relativistic system. The consequence of this quantum anomaly is the formation of bound state in the interval ξ\in(-1,1). The inequivalent quantization is characterized by a 1-parameter family of self-adjoint extension parameter Σ. We show that within the interval ξ\in(-1,1), cosmic string with zero radius can bind the dipole and the dipole does not fall into the singularity.

hep-th↗
arXiv2007

Scaling anomaly in cosmic string background

We show that the classical scale symmetry of a particle moving in cosmic string background is broken upon inequivalent quantization of the classical system, leading to anomaly. The consequence of this anomaly is the formation of single bound state in the coupling interval γ\in(-1,1). The inequivalent quantization is characterized by a 1-parameter family of self-adjoint extension parameter ω. It has been conjectured that the formation of loosely bound state in cosmic string background may lead to the so called anomalous scattering cross section for the particles, which is usually seen in molecular physics.

hep-th↗
arXiv2007

Electron Capture and Scaling Anomaly in Polar Molecules

We present a new analysis of the electron capture mechanism in polar molecules, based on von Neumann's theory of self-adjoint extensions. Our analysis suggests that it is theoretically possible for polar molecules to form bound states with electrons, even with dipole moments smaller than the critical value D_0 given by 1.63\times10^{-18} esu cm. This prediction is consistent with the observed anomalous electron scattering in H_2S and HCl, whose dipole moments are smaller than the critical value D_0. We also show that for a polar molecule with dipole moment less than D_0, typically there is only a single bound state, which is in qualitative agreement with observations. We argue that the quantum mechanical scaling anomaly is responsible for the formation of these bound states.

hep-th↗
arXiv2007

Quantum oscillator on complex projective space (Lobachewski space) in constant magnetic field and the issue of generic boundary conditions

We perform a 1-parameter family of self-adjoint extensions characterized by the parameter $ω_0$. This allows us to get generic boundary conditions for the quantum oscillator on $N$ dimensional complex projective space($\mathbb{C}P^N$) and on its non-compact version i.e., Lobachewski space($\mathcal L_N$) in presence of constant magnetic field. As a result, we get a family of energy spectrums for the oscillator. In our formulation the already known result of this oscillator is also belong to the family. We have also obtained energy spectrum which preserve all the symmetry (full hidden symmetry and rotational symmetry) of the oscillator. The method of self-adjoint extensions have been discussed for conic oscillator in presence of constant magnetic field also.

hep-th↗
arXiv2007

Asymptotic quasinormal modes of a noncommutative geometry inspired Schwarzschild black hole

We study the asymptotic quasi-normal modes for the scalar perturbation of the non-commutative geometry inspired Schwarzschild black hole in (3+1) dimensions. We have considered $M\geq M_0$, which effectively correspond to a single horizon Schwarzschild black hole with correction due to non-commutativity. We have shown that for this situation the real part of the asymptotic quasi-normal frequency is proportional to $\ln (3)$. The effect of non-commutativity of spacetime on quasi-normal frequency arises through the constant of proportionality, which is Hawking temperature $T_H(θ)$. We also consider the two horizon case and show that in this case also the real part of the asymptotic quasi-normal frequency is proportional to $\ln(3)$.

hep-th↗
arXiv2006

Generalized Solutions for Quantum Mechanical Oscillator on Kähler Conifold

We study the possible generalized boundary conditions and the corresponding solutions for the quantum mechanical oscillator model on Kähler conifold. We perform it by self-adjoint extension of the the initial domain of the effective radial Hamiltonian. Remarkable effect of this generalized boundary condition is that at certain boundary condition the orbital angular momentum degeneracy is restored! We also recover the known spectrum in our formulation, which of course correspond to some other boundary condition.

hep-th↗