arXiv subjects

Manjari Dutta

Publications and source records attributed to Manjari Dutta.

10 recordsLinked to original sources

arXiv2026

Some Studies On Exact Solutions Of Models In Noncommutative Spaces

The central theme of my thesis is to explore various simple prototype models that are exactly solvable in the framework of time dependent noncommutative spaces. By adopting the methodology provided by the Lewis Riesenfeld theory, we developed a procedure for obtaining a class of exact solutions for such model systems. We analyzed these solutions by deriving the energy expectation values analytically and representing those energy dynamics graphically. We also examined the explicit existence of a non-zero Berry geometric phase in the noncommutative framework and analyzed the role of noncommutativity in generating a non-trivial Berry phase when the model Hamiltonian and the noncommutative parameters are periodic in time. Overall, my thesis contributes to a deeper understanding of quantum theory in time dependent noncommutative backgrounds and indicates a strong possibility for developing a consistent quantum theory within such frameworks.

quant-ph↗

arXiv2026

Quantum regression theorem in the Unruh-DeWitt battery

In this paper, we employ the quantum regression theorem, a powerful tool in the study of open quantum systems, to analytically study the correlation functions of an Unruh-DeWitt detector, which is an uniformly accelerated two-level quantum system, absorbing charges from an external classical coherent pulse. The system can thus be viewed as a relativistic quantum battery that interacts with the environment of its perceived particles, namely, the quanta of a massless scalar field. By considering the relativistic battery moving in Rindler spacetime, under Born-Markov approximation, we derive the Gorini-Kossakowski-Sudarshan-Lindblad master equation governing the evolution of the system's reduced density matrix. Moreover, we perform the Fourier transformation of the Wightman functions and use exponential regularisation to compute the functional forms appearing in the master equation. Next, we derive the evolution equations for the the single-time expectation values of the system's operators. We not only solve these equations to find out the single time averages, but also employ the quantum regression theorem to determine the two-time correlation functions of first and second order. We analyse them to explain the phenomenon of spontaneous emission and show analytically how the acceleration can enhance the associated dissipation. Furthermore, we address a special form of second order correlation function relevant to the context of photon bunching arising in Bose-Einstein statistics. We analysed the results both analytically and graphically. Finally, we derive the spontaneous emission spectrum of the battery detector analytically, which in the long-time limit displays a well-defined Lorentzian line shape in the high frequency regime.

quant-ph↗

arXiv2026

Quasi-normal modes of quantum gravity black hole with perfectly fluid dark matter

In this work, we have studied the motion of a massless scalar photon in the renormalization group (RG) improved Schwarzschild black hole spacetime in the presence of perfectly fluid dark matter (PFDM). Considering the critical orbit conditions and the null geodesics condition in static spherically sym- In metric geometry, we have shown the variation of the radius of the photon sphere $r_{ph}$ with the PFDM parameter $\zeta$. Due to perturbations in black hole spacetime, gravitational waves are emitted in the form of quasi-normal radiations, which correspond to quasi-normal modes (QNMs). In this work, we have studied two types of perturbations in RG improved Schwarzschild spacetime: scalar field perturbations and electromagnetic (EM) field perturbations. For both cases, we have studied the effect of the PFDM parameter on the quasi-normal mode frequencies and the shadow of the black hole, which is related to the photon radius.

gr-qc↗

arXiv2025

Density matrix analysis of systems influenced by periodic Hamiltonians

In this work, we consider simple systems that are influenced by Hamiltonians with time periodicity. Our analysis is mainly focussed on the density matrix approach and aims to solve the Liouville equation of motion from which one can extract the state of the system when the system is in a pure state. We start our analysis with the standard Rabi-oscillation problem. We consider a density matrix corresponding to the entire model system and solve the Liouville equation of motion. We have then made use of the Lewis-Reisenfeld invariant approach and arrive at the exact same result which implies that the density matrix of the system can indeed be identified with the Lewis invariant. Finally, we consider a two-level system with a constant magnetic field in the $z$-direction and a time dependent magnetic field in the $x$-direction. Finally, we solve the Liouville equation of motion for this system and calculate the various coherence measures and plot them to investigate the time dependence and reliability of different coherence measures.

quant-ph↗

arXiv2025

Area spectrum and black hole thermodynamics

The role of horizon area quantization on black hole thermodynamics is investigated in this article. The coefficient appearing in the quantization of area is fixed by an appeal to the saturated form of the Landauer's principle. Then by considering transition between discrete states of the event horizon area which in turn is equivalent to transitions between discrete mass states of the black hole, the change in the mass can be obtained. The change in mass is then equated to the product of the Hawking temperature and change in entropy of the black hole between two consecutive discrete states applying the first law of black hole thermodynamics. This gives the corrected Hawking temperature. In particular, we apply this technique to the Schwarzschild black hole, the quantum corrected Schwarzschild black hole, the Reissner-Nordstr\"{o}m black hole which is a charged black hole, and the rotating Kerr black hole geometry, and obtain the corrected Hawking temperature in each of these cases. We then take a step forward by inserting this corrected Hawking temperature in the first law of black hole thermodynamics once again to calculate the entropy of the black hole in terms of the horizon area of the black hole. This leads to logarithmic and inverse corrections to the entropy of the black hole.

gr-qc↗

arXiv2024

Quantum harmonic oscillator in a time dependent noncommutative background

This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in [1]. Specifically, we examine the system when expressed in terms of commutative variables, utilizing a generalized form of the standard Bopp-shift relations recently introduced in [2]. We solved the time dependent system and obtained the analytical form of the eigenfunction using the method of Lewis invariants, which is associated with the Ermakov-Pinney equation, a non-linear differential equation. We then obtain exact analytical solution set for the Ermakov-Pinney equation. With these solutions in place, we move on to compute the dynamics of the energy expectation value analytically and explore their graphical representations for various solution sets of the Ermakov-Pinney equation, associated with a particular choice of quantum number. Finally, we determined the generalized form of the uncertainty equality relations among the operators for both commutative and noncommutative cases. Expectedly, our study is consistent with the findings in [1], specifically in a particular limit where the coordinate mapping relations reduce to the standard Bopp-shift relations.

quant-ph↗

arXiv2023

Lewis and Berry phases for a gravitational wave interacting with a quantum harmonic oscillator

In this work, we consider a gravitational wave interacting with a quantum harmonic oscillator in the transverse-traceless gauge. We take the gravitational wave to be carrying the signatures of both plus and cross polarization at first. We then try to obtain a suitable form of the Lewis invariant using the most general form possible while considering only quadratic order contributions from both position and momentum variables. In order to progress further, we then drop the cross terms obtaining a separable Hamiltonian in terms of the first and the second spatial coordinates. We then obtain two Lewis invariants corresponding to each separable parts of the entire Hamiltonian of the system. Using both Lewis invariants, one can obtain two Ermakov-Pinney equations, from which we finally obtain the corresponding Lewis phase and eventually the Berry phase for the entire system. Finally, we obtain some explicit expressions of the Berry phase for a plane polarized gravitational wave with different choices of the harmonic oscillator frequency.

hep-th↗

arXiv2021

Exact solution of damped harmonic oscillator with a magnetic field in a time dependent noncommutative space

In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in the presence of an external magnetic field varying with respect to time in time dependent noncommutative space. It has been observed that for some specific choices of the damping factor, the time dependent frequency of the oscillator and the time dependent external magnetic field, there exists interesting solutions of the time dependent noncommutative parameters following from the solutions of the Ermakov-Pinney equation. Further, these solutions enable us to get exact analytic forms for the phase which relates the eigenstates of the Hamiltonian with the eigenstates of the Lewis invariant. Then we compute the expectation value of the Hamiltonian. The expectation values of the energy are found to vary with time for different solutions of the Ermakov-Pinney equation corresponding to different choices of the damping factor, the time dependent frequency of the oscillator and the time dependent applied magnetic field. We also compare our results with those in the absence of the magnetic field obtained earlier.

quant-ph↗

arXiv2020

Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space

In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in time dependent noncommutative space. It has been observed that for some specific choices of the damping factor and the time dependent frequency of the oscillator, there exists interesting solutions of the time dependent noncommutative parameters following from the solutions of the Ermakov-Pinney equation. Further, these solutions enable us to get exact analytic forms for the phase which relates the eigenstates of the Hamiltonian with the eigenstates of the Lewis invariant. We then obtain expressions for the matrix elements of the coordinate operators raised to a finite arbitrary power. From these general results we then compute the expectation value of the Hamiltonian. The expectation values of the energy are found to vary with time for different solutions of the Ermakov-Pinney equation corresponding to different choices of the damping factor and the time dependent frequency of the oscillator.

quant-ph↗

arXiv2019

Photon velocity, power spectrum in Unruh effect with modified dispersion relation

In this paper we propose a new form of generalized uncertainty principle which involves both a linear as well as a quadratic term in the momentum. From this we have obtained the corresponding modified dispersion relation which is compared with the corresponding relation in rainbow gravity. The new form of the generalized uncertainty principle reduces to the known forms in appropriate limits. We then calculate the modified velocity of photons and we find that it is energy dependent, allowing therefore for a superluminal propagation. We then derive the $1+1$-dimensional Klein-Gordon equation taking into account the effects of the modified dispersion relation. The positive frequency mode solution of this equation is then used to calculate the power spectrum arising due to the Unruh effect. The result shows that the power spectrum depends on the energy of the particle owing its origin to the presence of the generalized uncertainty principle. Our results capture the effects of both the simplest form as well as the linear form of the generalized uncertainty principle and also points out an error in the result of the power spectrum up to first order in the generalized uncertainty principle parameter existing in the literature.

physics.gen-ph↗