arXiv subjects
Publications and source records attributed to Bijan Bagchi.
The modified Newtonian dynamics (MOND) paradigm is discussed in the context of asymptotic safe gravity. We estimate quantum correction to the logarithmic potential which is well known to account for the constancy of the circular velocity $v$ of the spiral galaxies. We determine plausible bounds on $v$.
We examine the possibility of artificial Hawking radiation by proposing a non-PT - symmetric weakly pseudo-Hermitian two band model containing a tilting parameter. We also determine the tunneling probability using our Hamiltonian through the event horizon that acts as a classically forbidden barrier.
We investigate the (1+1)-dimensional position-dependent mass Dirac equation within the confines of so(2,1) potential algebra by utilizing the character of a spatial varying Fermi velocity. We examine the combined effects of the two when the Dirac equation is equipped with an external pseuodoscalar potential. Solutions of the three cases induced by so(2, 1) are explored by profitably making use of a point canonical transformation.
We propose an interacting nonhermitian model described by a two-mode quadratic Hamiltonian along with an interaction term to locate and analyze the presence of an exceptional point in the system. Each mode is guided by a Swanson-like quadratic Hamiltonian and a suitable choice is made for the interaction term. The parity-time symmetric transformation is adopted in the standard way relevant for a coupled system.
We solve the one-dimensional Dirac equation by taking into account the possibility of position-dependence in the mass function. We also take the Fermi velocity to act as a local variable and examine the combined effects of the two on the solvability of the Dirac equation with respect to the Morse potential. Our results for the wave functions and the energy levels corresponding to such an extended scheme are furnished in closed forms.
We re-examine Hawking radiation for a nonrotating (2+1)-dimensional BTZ black hole and evaluate the transmission probability of tunneling through the barrier of the event horizon employing the standard method of WKB approximation. Our results are presented for both uncharged and charged cases. We also explore the associated thermodynamics in terms of Hawking temperature and provide estimates of black hole parameters like the surface gravity and entropy.
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative analysis of orbits around the equilibrium points, period-doubling bifurcation, time series curves, surfaces of section and Poincare maps. An interesting outcome of our findings is the emergence of chaotic behavior when the system is confronted with a periodic force term like fcosωt.
We investigate the most general form of the one-dimensional Dirac Hamiltonian $H_D$ in the presence of scalar and pseudoscalar potentials. To seek embedding of supersymmetry (SUSY) in it, as an alternative procedure to directly employing the intertwining relations, we construct a quasi-Hamiltonian $\mathcal{K}$, defined as the square of $H_D$, to explore the consequences. We show that the diagonal elements of $\mathcal{K}$ under a suitable approximation reflects the presence of a superpotential thus proving a useful guide in unveiling the role of SUSY. For illustrative purpose we apply our scheme to the transformed one-dimensional version of the planar electron Hamiltonian under the influence of a magnetic field. We generate spectral solutions for a class of isochronous potentials.
We extend Fring-Tenney approach of constructing invariants of constant mass time-dependent system to the case of a time-dependent mass particle. From a coupled set of equations described in terms of guiding parameter functions, we track down a modified Ermakov-Pinney equation involving a time-dependent mass function. As a concrete example we focus on an exponential choice of the mass function.
This review is intended for readers who want to have a quick understanding on the theoretical underpinnings of coherent states and squeezed states which are conventionally generated from the prototype harmonic oscillator but not always restricting to it. Noting that the treatments of building up such states have a long history, we collected the important ingredients and reproduced them from a fresh perspective but refrained from delving into detailed derivation of each topic. By no means we claim a comprehensive presentation of the subject but have only tried to re-capture some of the essential results and pointed out their inter-connectivity.
New families of non-parity-time-symmetric complex potentials with all-real spectra are derived by the supersymmetry method and the pseudo-Hermiticity method. With the supersymmetry method, we find families of non-parity-time-symmetric complex partner potentials which share the same spectrum as base potentials with known real spectra, such as the (complex) Wadati potentials. Different from previous supersymmetry derivations of potentials with real spectra, our derivation does not utilize discrete eigenmodes of base potentials. As a result, our partner potentials feature explicit analytical expressions which contain free functions. With the pseudo-Hermiticity method, we derive a new class of non-parity-time-symmetric complex potentials with free functions and constants, whose eigenvalues appear as conjugate pairs. This eigenvalue symmetry forces the spectrum to be all-real for a wide range of choices of these functions and constants in the potential. Tuning these free functions and constants, phase transition can also be induced, where conjugate pairs of complex eigenvalues emerge in the spectrum.
We show in this paper that the basic representations of position and momentum in a quantum mechanical system, that are guided by a generalized uncertainty principle and lead to a corresponding one-parameter eigenvalue problem, can be interpreted in terms of an extended Schrodinger equation embodying momentum-dependent mass. Some simple consequences are pointed out.
Working within the framework of parity-time-symmetric quantum mechanics we look into the possibility of entanglement generation and demonstrate that the feature of non-violation of no-signaling principle may hold for the simplest non-trivial case of bipartite systems. Basically our arguments are based on the computation of the reduced density matrix of one party to justify that the entropy of the other does not change.
The evolution operator U(t) for a time-independent parity-time-symmetric systems is well studied in the literature. However, for the non-Hermitian time-dependent systems, a closed form expression for the evolution operator is not available. In this paper, we make use of a procedure, originally developed by A.R.P. Rau [Phys.Rev.Lett, 81, 4785-4789 (1998)], in the context of deriving the solution of Liuville-Bloch equations in the product form of exponential operators when time-dependent external fields are present, for the evaluation of U(t) in the interaction picture wherein the corresponding Hamiltonian is time-dependent and in general non-Hermitian. This amounts to a transformation of the whole scheme in terms of addressing a nonlinear Riccati equation the existence of whose solutions depends on the fulfillment of a certain accompanying integrabilty condition.
We point out that when a quadratic type Liénard equation is suitably interpreted shows branching due to the double valuedness of the governing Hamiltonian. Under certain approximation of the guiding coupling constant we derive its quantum counterpart that is guided by a momentum-dependent mass function.
Quantum and noncommutative corrections to the Newtonian law of inertia are considered in the general setting of Verlinde's entropic force postulate. We demonstrate that the form for the modified Newtonian dynamics (MOND) emerges in a classical setting by seeking appropriate corrections in the entropy.We estimate the correction term by using concrete coherent states in the standard and generalized versions of Heisenberg's uncertainty principle. Using Jackiw's direct and analytic method we compute the explicit wavefunctions for these states producing minimal length as well as minimal products. Subsequently we derive a further selection criterion restricting the free parameters in the model in providing a canonical formulation of the quantum corrected Newtonian law by setting up the Lagrangian and Hamiltonian for the system.
It is proved the equivalence of the compatibility condition of [A. Ramos, J. Phys. A 44 (2011) 342001, Phys. Lett. A 376 (2012) 3499] with a condition found in [Yadav et al., Ann. Phys. 359 (2015) 46]. The link of Shape Invariance with the existence of a Potential Algebra is reinforced for the rationally extended Shape Invariant potentials. Some examples on X1 and Xl Jacobi and Laguerre cases are given.
Hamiltonians that are multivalued functions of momenta are of topical interest since they correspond to the Lagrangians containing higher-degree time derivatives. Incidentally, such classes of branched Hamiltonians lead to certain not too well understood ambiguities in the procedure of quantization. Within this framework, we pick up a model that samples the latter ambiguities and simultaneously turns out to be amenable to a transparent analytic and perturbative treatment.