arXiv subjects

Kaushik Bhattacharya

Publications and source records attributed to Kaushik Bhattacharya.

At least 145 records · Page 8Linked to original sources

arXiv2011

Length contraction in Very Special Relativity

Glashow and Cohen claim that many results of special theory of relativity (SR) like time dilation, relativistic velocity addition, etc, can be explained by using certain proper subgroups, of the Lorentz group, which collectively form the main body of Very special relativity (VSR). They did not mention about length contraction in VSR. Length contraction in VSR has not been studied at all. In this article we calculate how the length of a moving rod contracts in VSR, particularly in the HOM(2) version. The results are interesting in the sense that in general the length contraction formulas in VSR are different from SR but in many cases the two theories predict similar length contraction of moving rods.

physics.class-ph↗

arXiv2011

Possible potentials responsible for stable circular relativistic orbits

Bertrand's theorem in classical mechanics of the central force fields attracts us because of its predictive power. It categorically proves that there can only be two types of forces which can produce stable, circular orbits. In the present article an attempt has been made to generalize Bertrand's theorem to the central force problem of relativistic systems. The stability criterion for potentials which can produce stable, circular orbits in the relativistic central force problem has been deduced and a general solution of it is presented in the article. It is seen that the inverse square law passes the relativistic test but the kind of force required for simple harmonic motion does not. Special relativistic effects do not allow stable, circular orbits in presence of a force which is proportional to the negative of the displacement of the particle from the potential center.

physics.class-ph↗

arXiv2010

Disclination-mediated thermo-optical response in nematic glass sheets

Nematic solids respond strongly to changes in ambient heat or light, significantly differently parallel and perpendicular to the director. This phenomenon is well characterized for uniform director fields, but not for defect textures. We analyze the elastic ground states of a nematic glass in the membrane approximation as a function of temperature for some disclination defects with an eye towards reversibly inducing three-dimensional shapes from flat sheets of material, at the nano-scale all the way to macroscopic objects, including non-developable surfaces. The latter offers a new paradigm to actuation via switchable stretch in thin systems.

cond-mat.soft↗

arXiv2009

Gauge transformation through an accelerated frame of reference

The Schrödinger equation of a charged particle in a uniform electric field can be specified in either a time-independent or a time-dependent gauge. The wave-function solutions in these two gauges are related by a phase-factor reflecting the gauge symmetry of the problem. In this article we show that the effect of such a gauge transformation connecting the two wave-functions can be mimicked by the effect of two successive extended Galilean transformations connecting the two wave-function. An extended Galilean transformation connects two reference frames out of which one is accelerating with respect to the other.

quant-ph↗

arXiv2009

The electric charge and magnetic moment of neutral fundamental particles

The article focuses on the issue of the two definitions of charge, mainly the gauge charge and the effective charge of fundamental particles. Most textbooks on classical electromagnetism and quantum field theory only works with the gauge charges while the concept of the induced charge remains unattended. In this article it has been shown that for intrinsically charged particles both of the charges remain the same but there can be situations where an electrically neutral particle picks up some electrical charge from its plasma surrounding. The physical origin and the scope of application of the induced charge concept has been briefly discussed in the article.

hep-ph↗

arXiv2008

Neutrino absorption by W production in the presence of a magnetic field

In this work we calculate the decay rate of the electron type neutrinos into $W$ bosons and electrons in presence of an external uniform magnetic field. The decay rate is calculated from the imaginary part of the $W$ exchange neutrino self-energy diagram but in the weak field limit and compare our result with the existing one.

hep-ph↗

arXiv2008

Origin of undesirable cracks during layer transfer

We investigate the origin of undesirable transverse cracks often observed in thin films obtained by the layer transfer technique. During this process, two crystals bonded to each other containing a weak plan produced by ion implantation are heated to let a thin layer of one of the material on the other. The level of stress imposed on the film during the heating phase due to the mismatch of thermal expansion coefficients of the substrate and the film is shown to be the relevant parameter of the problem. In particular, it is shown that if the film is submitted to a tensile stress, the microcracks produced by ion implantation are not stable and deviate from their straight trajectory making the layer transfer process impossible. However, if the compressive stress exceeds a threshold value, after layer transfer, the film can buckle and delaminate, leading to transverse cracks induced by bending. As a result, we show that the imposed stress σ_m - or equivalently the heating temperature - must be within the range -σ_c < σ_m < 0 to produce an intact thin film where σ_c depends on the interfacial fracture energy and the size of defects at the interface between film and substrate.

physics.class-ph↗

arXiv2008

Some intricacies of the momentum operator in quantum mechanics

quant-ph↗

arXiv2008

The neutrino self-energy in a magnetized medium

In this work we calculate the neutrino self-energy in presence of a magnetized medium. The magnetized medium consists of electrons, positrons, neutrinos and a uniform classical magnetic field. The calculation is done assuming the background magnetic field is weak compared to the $W$-Boson mass squared, as a consequence of which only linear order corrections in the field are included in the $W$ boson propagator. The electron propagator consists all order corrections in the background field. Although the neutrino self-energy in a magnetized medium in various limiting cases has been calculated previously in this article we produce the most general expression of the self-energy in absence of the Landau quantization of the charged gauge fields. We calculate the effect of the Landau quantization of the charged leptons on the neutrino self-energy in the general case. Our calculation is specifically suited for situations where the background plasma may be CP symmetric.

hep-ph↗

arXiv2007

Neutrino self-energy in a magnetized charge-symmetric medium

In this talk we present the calculation of the neutrino self-energy in presence of a magnetized medium. The magnetized medium consists of electrons, positrons, neutrinos and a uniform classical magnetic field. The background magnetic field is assumed to be weak compared to the $W$-Boson mass as a consequence of which only linear order corrections in the field are included in the $W$ boson propagator. The electron propagator consists all order corrections in the background field. Our calculation is specifically suited for situations where the background plasma may be CP symmetric.

hep-ph↗

arXiv2007

Solution of the Dirac equation in presence of an uniform magnetic field

In this work we discuss the properties of the solutions of the Dirac equation in presence of an uniform background magnetic field. In particular we focus on the nature of the solutions, their ortho-normality properties and how these solutions depend on the choice of the vector potential giving rise to the magnetic field. We explicitly calculate the spin-sum of the solutions and using it we calculate the propagator of the electron in presence of an uniform background magnetic field.

hep-th↗

arXiv2007

Reality of linear and angular momentum expectation values in bound states

In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian prescription to other coordinates and falls in a trap. In this work we introduce the difficulties one faces when the question of the momentum operator in spherical polar coordinate comes. We have tried to point out most of the elementary quantum mechanical results, related to the momentum operator, which has coordinate dependence. We explicitly calculate the momentum expectation values in various bound states and show that the expectation value really turns out to be zero, a consequence of the fact that the momentum expectation value is real. We comment briefly on the status of the angular variables in quantum mechanics and the problems related in interpreting them as dynamical variables. At the end, we calculate the Heisenberg's equation of motion for the radial component of the momentum for the Hydrogen atom.

quant-ph↗

arXiv2006

Enhanced polarization of CMB from thermal gravitational waves

If inflation was preceded by a radiation era then at the time of inflation there will exist a decoupled thermal distribution of gravitons. Gravitational waves generated during inflation will be amplified by the process of stimulated emission into the existing thermal distribution of gravitons. Consequently the usual zero temperature scale invariant tensor spectrum is modified by a temperature dependent factor. This thermal correction factor amplify the $B$-mode polarization of the CMB by an order of magnitude at large angles, which may now be in the range of observability of WMAP.

astro-ph↗

arXiv2006

Leptogenesis and low energy CP phases with two heavy neutrinos

An attractive explanation for non-zero neutrino masses and small matter antimatter asymmetry of the present Universe lies in "leptogenesis". At present the {\it size} of the lepton asymmetry is precisely known, while the {\it sign} is not known yet. In this work we determine the sign of this asymmetry in the framework of two right handed neutrino models by relating the leptogenesis phase(s) with the low energy CP violating phases appearing in the leptonic mixing matrix. It is shown that the knowledge of low energy lepton number violating re-phasing invariants can indeed determine the sign of the present matter antimatter asymmetry of the Universe and hence indirectly probing the light physical neutrinos to be Majorana type.

hep-ph↗

arXiv2006

See-saw fermion masses in an SO(10) GUT

In this work we study an SO(10) GUT model with minimum Higgs representations belonging only to the 210 and 16 dimensional representations of SO(10). We add a singlet fermion S in addition to the usual 16 dimensional representation containing quarks and leptons. There are no Higgs bi-doublets and so charged fermion masses come from one-loop corrections. Consequently all the fermion masses, Dirac and Majorana, are of the see-saw type. We minimize the Higgs potential and show how the left-right symmetry is broken in our model where it is assumed that a D-parity odd Higgs field gets a vacuum expectation value at the grand unification scale. From the renormalization group equations we infer that in our model unification happens at 10^{15} GeV and left-right symmetry can be extended up to some values just above 10^{11} GeV. The Yukawa sector of our model is completely different from most of the standard grand unified theories and we explicitly show how the Yukawa sector will look like in the different phases and briefly comment on the running of the top quark mass. We end with a brief analysis of lepton number asymmetry generated from the interactions in our model.

hep-ph↗

arXiv2006

Temperature of the inflaton and duration of inflation from WMAP data

If the initial state of the inflaton field is taken to have a thermal distribution instead of the conventional zero particle vacuum state then the curvature power spectrum gets modified by a temperature dependent factor such that the fluctuation spectrum of the microwave background radiation is enhanced at larger angles. We compare this modified cosmic microwave background spectrum with Wilkinson microwave anisotropy probe data to obtain an upper bound on the temperature of the inflaton at the time our current horizon crossed the horizon during inflation. We further conclude that there must be additional e-foldings of inflation beyond what is needed to solve the horizon problem.

hep-ph↗

arXiv2006

Decay of Spin-One Particle into Two Photons in Presence of Uniform External Magnetic Field

Yang's theorem states that an initial J=1 state cannot decay into two photons. Because of this result some reactions relating to elementary particles or atomic transitions can be ruled out. The theorem is not valid in the presence of background electric or magnetic fields. In this work we show that the decay of a J=1 particle into two photons is permitted by Bose symmetry and rotational invariance when the background of the decay process is not pure vacuum but contains an external classical magnetic/electric field. We also discuss constraints on these amplitudes from {\bf CP} invariance.

hep-ph↗

arXiv2005

Gauge invariance of elementary particle processes taking place in presence of a background magnetic field

Elementary particle scatterings and decays in presence of a background magnetic field are very common in physics, specially after the observation that the core of the neutron stars can sustain a magnetic field of the order of $10^{13} {\rm G}$. The important point about these calculations is that they are done in a background of a gauge field and as a result the calculations are prone to gauge arbitrariness. In this work we will investigate how this gauge arbitrariness is eradicated in processes where the initial and final particles taking part in the interactions are electrically neutral. Some comments on those processes where the initial or final state consists of electrically charged particles is presented at the end of the article.

hep-ph↗