arXiv subjects

Somenath Chakrabarty

Publications and source records attributed to Somenath Chakrabarty.

At least 19 recordsLinked to original sources

arXiv2020

Schroedinger Equation and the Associated Physics in Non-Inertial Frame

In this article we have developed a formalism to obtain the solution of Schroedinger equation in a non-inertial frame. The frame is moving relative to an inertial frame with an acceleration. The formulation has been developed using Lagrangian formalism as discussed in Classical Mechanics book by Landau and Lifshitz [1]. Hence we have obtained the Hamiltonian of the nucleons. Then using the standard form of canonical quantization rule, we have setup the Schroedinger equation in non-inertial frame. In the present study we have considered only the accelerated rectilinear motion of the non-inertial frame. The rotation will be considered in some future work based on quantum field theory [2] (see also [3, 4]). We therefore drop the rotation part of the Hamiltonian in our calculation. The physically acceptable result on our work is basically the solution obtained by Fowler and Nordheim for the emission of electrons from cold metal surface induced by strong electric field [5] known as cold field emission of electrons. However in the present formulation, it is the gravity which acts on mass of the particle and causes emission. The centrifugal force acts like gravity. Hence we have got some flavor of Hawking radiation [6] and also Unruh effect [7] within the limited scope of our non-relativistic approach. We have also shown that relative motion of a two body quantum mechanical system does not depend on the nature of the frame of reference.

physics.gen-ph↗

arXiv2019

Time Dependent Rindler Hamiltonian Eigen States in Momentum Space

We have developed a formalism to get the time evolution of the eigen states of Rindler Hamiltonian in momentum space. We have shown the difficulties with characteristic curves, and re-cast the time evolution equations in the form of two-dimensional Laplace equation. The solutions are obtain both in polar coordinates as well as in the Cartesian form.

gr-qc↗

arXiv2019

On the Eigen Value Problem in Rindler Space

In this article in a very general manner we have investigated the eigen value problem in Rindler space. We have developed the formalism in an exact form. It has been noticed that although the Hamiltonian is non-hermitian, because of the PT-symmetric nature, the eigen values are real, where P and T are the parity operator and the time reversal operator respectively. It has further been observed that the eigen energies are linearly quantized and the binding of the system increases with the increase in the strength of uniform gravitational field although its origin is purely classical.

gr-qc↗

arXiv2018

Saha Equation for the Photo-Ionization of Hydrogen Atoms in Partially Ionized Relativistic Hydrogen Plasma and the Effect of Gravity on the Binding of Hydrogen Atoms in Rindler Space

We have studied Saha equation for photo-ionization of hydrogen atoms in partially ionized relativistic hydrogen plasma in Rindler space. Following the principle of equivalence, we have obtained the abundances of neutral hydrogen atoms, hydrogen ions and the electrons in dynamic equilibrium of the photo-ionization reaction of neutral hydrogen atoms and electron capture process by hydrogen ions (de-ionization process) and also investigated their variations with temperature of the plasma and the uniform gravitational field in the Rindler space or equivalently the uniform acceleration of the observer. Hence obtained the Saha ionization formula for partially ionized hydrogen plasma in Rindler space. It has been observed that the abundance of neutral hydrogen atoms decreases with the increase in temperature of the plasma, which is the usual picture, whereas it increases with the increases in the strength of uniform gravitational field. The second part of this observation shows that the binding of the electrons inside hydrogen atoms increases with the increase in the strength of gravitational field or equivalently an observer with very high acceleration will see less amount of ionized hydrogen atoms compared to inertial observer.

gr-qc↗

arXiv2017

Thomas-Fermi Model in Rindler Space

In this article we have investigated the Thomas-Fermi model for the electron gas in Rindler space. We have found that if the uniform acceleration is along $+x$-direction, then there is $y-z$-symmetry in space. For the sake of mathematical simplicity, we have assumed two dimensional spatial structure ($x-y$) in Rindler space. It has been observed that in two dimensional spatial coordinates the electrons are distributed discontinuously but in a periodic manner in a number of rectangular strips like domain along $\pm y$-direction. Some of them are having void structure, with no electrons inside such rectangular strips, while some are filled with electrons. We call the later type domain as the normal zone. We have also given physical interpretation for such exotic type electron distribution in Rindler space.

gr-qc↗

arXiv2017

The Propagation of de Broglie Waves in Rindler Space

In this article we have studied the propagation of matter waves in Rindler space. We have also developed the formalism to obtained space dependent refractive index for de Broglie waves for the particle and shown the possibility of particle emission from the event horizon of classical black holes, when observed from a uniformly accelerated frame.

gr-qc↗

arXiv2017

Motion of Massive Particles in Rindler Space and the Problem of Fall at the Centre

The motion of a massive particle in Rindler space has been studied and obtained the geodesics of motion. The orbits in Rindler space are found to be quite different from that of Schwarzschild case. The paths are not like the Perihelion Precession type. Further we have set up the non-relativistic Schrodinger equation for the particle in the quantum mechanical scenario in presence of background constant gravitational field and investigated the problem of fall of the particle at the center. This problem is also treated classically. Unlike the conventional scenario, here the fall occurs at the surface of a sphere of unit radius.

physics.gen-ph↗

arXiv2017

Saha Equation in Rindler Space

The Saha equations for photo-ionization process of hydrogen atoms and the creation of electron-positron pairs at high temperature are investigated in a reference frame undergoing a uniform accelerated motion in an otherwise flat Minkowski space-time geometry or equivalently, in a rest frame in presence of a strong uniform gravitational field. It is known as the Rindler space.

astro-ph.HE↗

arXiv2017

On The Transport Theory of Classical Gases in Rindler Space

We have obtained the Vlasov equation and Boltzmann kinetic equation using Poisson bracket (classical Hamilton equation) and Rindler Hamiltonian. Further, we treat the whole Universe as a statistical system with galaxies as the point particle constituents in large scale structure. Since the collisions of galaxies are very rare phenomena, we assume that the gas with the constituents as point galaxies satisfy Vlasov equation. Considering the astrophysical catastrophic event, e.g., the creation of gravity waves by the collisions of black holes, and further assuming that when such a wave passes through the gas causes a kind of polarization of mass distribution. This polarization of mass distribution will further gives rise to gravitational permittivity or dielectric constant. We have shown that the low frequency gravity waves will be absorbed, whereas the high frequency part will pass through the gas of point galaxies. It is further noticed that the region in space with extremely high gravitational field is transparent to gravity waves. In the other part of this work, using the Boltzmann equation and replacing the collision term by the relaxation time approximation and further assuming a small deviation from the equilibrium configuration of the stellar / galactic plasma in Rindler space, we have obtained the kinetic coefficients. For the first time we have derived an expression for the coefficient of gravitational flow. It has further been shown that in presence of strong gravitational field all the kinetic coefficients become vanishingly small.

physics.gen-ph↗

arXiv2017

The Thomas-Fermi and the Thomas-Fermi-Dirac Models in Two-Dimension- the Effect of Strong Quantizing Magnetic Field

Using Thomas-Fermi (TF) and Thomas-Fermi-Dirac (TFD) models, we have investigated the properties of electron gas inside two-dimensional (2D) Wigner-Seitz (WS) cells in presence of a strong orthogonal quantizing magnetic field. The electron-electron Coulomb exchange interaction in quasi-2D case is obtained. The exact form of exchange term in 2D is derived making the width of the system tending to zero. Further, using the exchange term, the Thomas-Fermi-Dirac equation in 2D is established. It has been observed that only the ionized WS cell can have finite radius in the Thomas-Fermi model, even in presence of a strong quantizing magnetic field. On the other hand, in the Thomas-Fermi-Dirac model a neutral WS cell can have finite radius.

astro-ph.SR↗

arXiv2016

Classical Trajectories in Rindler Space and Restricted Structure of Phase Space

The nature of single particle classical phase space trajectories in Rindler space have been studied. It has been shown that only a small portion of the phase space is accessible to the particles, whereas the major part of the phase space region is completely forbidden. It has also been noticed that the area / volume of the forbidden region of phase space increases with the increase in the strength of gravitational field. The physical significance of such squeezing of phase space in strong gravitational field has been discussed.

gr-qc↗

arXiv2016

Wien's Displacement Law in Rindler Space

In this article we have developed the formalisms for the modified form of Wien displacement laws for both the gas of electromagnetic waves and a gas of de Broglie waves in Rindler space. In the case of de Broglie waves we assume both fermion type and boson type materials. Following the classic work of Wien, we assume that the wall of the enclosure containing the photon gas or the gas of de Broglie waves, is expanding adiabatically with a uniform acceleration.

gr-qc↗

arXiv2016

Some Theoretical Aspects of Quantum Mechanical Equations in Rindler Space

In this article we have investigated some of the theoretical aspects of the solutions of quantum mechanical equations in Rindler space. We have developed the formalism for exact analytical solutions for Schr$\ddot{\rm{o}}$dinger equation and Klein-Gordon equation. Along with the approximate form of solutions for these two quantum mechanical equations. We have discussed the physical significance of our findings. The Hamiltonian operator in Rindler space is found to be non-Hermitian in nature. But the energy eigen values or the energy eigen spectra are observed to be real. We have noticed that the sole reason behind such real behavior is the PT symmetric form of the Hamiltonian operator.

gr-qc↗

arXiv2015

Fermat's Principle in Curved Space-time, No Emission from Schwarzschild Black Holes as Total Internal Reflection and Black Hole Unruh effect

Using the Fermat's principle in curved space-time with stationary type metric, we have obtained the speed of light as a function of spatial coordinates and hence the corresponding refractive index. The whole region with space dependent gravity is divided into a number of overlapping transparent refracting media with varying refractive index. The refractive index is found to be increasing with the strength of gravitational field. Hence using the laws of refraction, we have explained the gravitational bending of light. Further using the conventional idea of total internal reflection of light while going from denser to rarer medium, in the present scenario it is the propagation of light from the region of ultra-strong gravitational field to relatively weaker gravitational field region, we have proposed an alternative approach for no emission of any kind of electromagnetic radiation from the surface of a classical Schwarzschild Black Hole. We have further noticed that for an observer in a uniformly accelerated frame, analogous to the Unruh radiation, there can be emission of electromagnetic waves from the event horizon of a classical black hole. This may be named as "black hole Unruh effect".

gr-qc↗

arXiv2015

The Study of Two-dimensional Polytropic Stars

In this article we have studied the structure of hypothetical two-dimensional polytropic stars. Considering some academic interest, we have developed a formalism to investigate some of the gross properties of such stellar objects. However, we strongly believe that the formalism developed here may be prescribed as class problem for post-graduate level students in physics or a post-graduate dissertation project work in physics.

physics.gen-ph↗

arXiv2015

The Hawking Radiation as Gravitational Fowler-Nordheim Emission in Uniformly Accelerated Frame, in The Non-Relativistic Scenario

In the conventional scenario, the Hawking radiation is believed to be a tunneling process at the event horizon of the black hole. In the quantum field theoretic approach the Schwinger's mechanism is generally used to give an explanation of this tunneling process. It is the decay of quantum vacuum into particle anti-particle pairs near the black hole surface. However, in a reference frame undergoing an uniform accelerated motion in an otherwise flat Minkowski space-time geometry, in the non-relativistic approximation, the particle production near the event horizon of a black hole may be treated as a kind of Fowler-Nordheim field emission, which is the typical electron emission process from a metal surface under the action of an external electrostatic field. This type of emission from metal surface is allowed even at extremely low temperature. It has been noticed that in one-dimensional scenario, the Schr$\ddot{\rm{o}}$dinger equation satisfied by the created particle (anti-particle) near the event horizon, can be reduced to a differential form which is exactly identical with that obeyed by an electron immediately after the emission from the metal surface under the action of a strong electrostatic field. The mechanism of particle production near the event horizon of a black hole is therefore identified with Schwinger process in relativistic quantum field theory, whereas in the non-relativistic scenario it may be interpreted as Fowler-Nordheim emission process, when observed from an uniformly accelerated frame.

astro-ph.HE↗

arXiv2015

Schrödinger Equation of a particle in an Uniformly Accelerated Frame and the Possibility of a New kind of Quanta

In this article we have developed a formalism to obtain the Schr$\ddot{\rm{o}}$dinger equation for a particle in a frame undergoing an uniform acceleration in an otherwise flat Minkowski space-time geometry. We have presented an exact solution of the equation and obtained the eigenfunctions and the corresponding eigenvalues. It has been observed that the Schr$\ddot{\rm{o}}$dinger equation can be reduced to an one dimensional hydrogen atom problem. Whereas, the quantized energy levels are exactly identical with that of an one dimensional quantum harmonic oscillator. Hence considering transitions, we have predicted the existence of a new kind of quanta, which will either be emitted or absorbed if the particles get excited or de-excited respectively.

gr-qc↗

arXiv2015

Doppler Shift of the de Broglie Waves- Some New Results from Very Old Concepts

The Doppler shift of de Broglie wave is obtained for fermions and massive bosons using the conventional form of Lorentz transformations for momentum and energy of the particles. A formalism is developed to obtain the variation of wave length for de Broglie waves with temperature for individual particles using the classic idea of Wien in a many body Fermi gas or massive Bose gas.

cond-mat.quant-gas↗