Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Optics and Photonics

Time-Dependent Dissipative Massive Scalar Field

Marjan Jafari

Published Jan 1, 2021• 0 citations
Publisher

Abstract

In this work, we investigate a timedependent dissipative scalar field.Inspired by the Bateman lagrangian, we showed a procedure for quantizatizing the massive scalar field with the time-dependent dissipative term.So, the properties of a quantum dissipative scalar field are analyzed by the Caldirola-Kanai model.Also, we construct the Hilbert space for the system and calculate the wave eigen-functions and probability distribution of the system.

DOI
10.52547/ijop.15.1.49

Related papers

Finite temperature correlation function of two dissipative massive scalar fields: Thermofield approach

Marjan Jafari

The present paper aims at investigating the manner of two dissipative massive scalar fields. Two massive scalar fields that interact with a reservoir were considered and a reservoir was modeled by continuum Klein-Gordon fields. The Lagrangian of the total system was canonically quantized and the dynamics of the system was determined using the Euler-Lagrange equation. Then, the explicit form of the quantum massive scalar fields in long-time limit were observed. The propagator of the system and correlation functions were calculated at finite temperature in the thermofield dynamics formalizem.

•Dec 1, 2017•0 citations

Nonunitary connection between explicitly time-dependent and nonlinear approachesfor the description of dissipative quantum systems

Dieter Schuch

Caldirola [Nuovo Cimento 18, 393 (1941)] and Kanai's [Prog. Theor. Phys. 3, 440 (1948)] time-dependent approach for dissipative systems can be traced back to the conventional system-plus-reservoir approach; however, it apparently violates the uncertainty principle. This discrepancy can be avoided by considering a consistent transition between the Caldirola-Kanai formalism and a logarithmic nonlinear Schr\"odinger equation that requires not only a transformation of the operators, but also a nonunitary transformation of the wave function. This procedure also shows the equivalence of three at first sight incompatible approaches to describe dissipative quantum systems.

Physical Review A•Feb 1, 1997•69 citations

Non Commutative Quantum Mechanics in Time - Dependent Backgrounds

Antony Streklas

The problem of the dissipative systems from the quantum point of view has been of increasing interest, but it is far from having a satisfactory solution (1). There are many problems where the dissipation has an important role such as in quantum optics, in quantum analysis of fields, in quantum gravity (2). Dissipation can be observed in interactions between two systems, the observed system and another one often called reservoir or the bath, into which the energy flows via an irreversiblemanner (3). The system is embedded in some environmentwhich is in principle unknown. For an effective description of such systems, we can use time dependent Hamiltonians which in classical physics yield the proper equation of motion. If the friction is a linear funcion of the velocity with friction constant γ the Hamiltonian is the well known Caldirola Kanai Hamiltonian

InTech eBooks•Feb 24, 2012•3 citations

On the Quantum Mechanical Treatment of the Bateman-Morse-Feshbach Damped Oscillator with Variable Mass

Akira Suzuki, Hiroki Majima

The harmonic oscillator with time-dependent (indefinite and variable) mass subject to the force proportional to velocity is studied by extending Bateman’s dual Lagrangian and Hamiltonian formalism. To study the quantum analog of such a dissipative system, the Batemann-Morse-Feshback classical Hamiltonian of the damped harmonic oscillator with varying (time-dependent) mass is canonically quantized. In order to discuss the stability of the quantum dissipative system due to the influence of varying mass and the dissipative force, we derived a formula for the vacuum state of the dissipative system with the help of quantum field theoretical framework. It is shown that the formula based on this simple model could be used to study the influence of dissipation such as the instability due to the dissipative force and/or the variable mass. It is understood that the change in the oscillator mass corresponds to a control parameter in quantum dissipative systems.

Journal of Modern Physics•Jan 1, 2016•3 citations

Dissipative Dynamics and Uncertainty Measures of a Charged Oscillator in the Presence of the Aharonov-Bohm Effect

J. P. G. Nascimento, V. Aguiar, D. S. Cortez +1 more

We analyze the effects of dissipation in a charged oscillator in the presence of the Aharonov-Bohm effect by using time-dependent mass (m(t)) Hamiltonians. We consider two different models for the dissipative Hamiltonian and analyze the uncertainties (Δr and Δp) and the quantum mechanical expectation value of energy (⟨E⟩) in terms of time (t), damping parameters and flux parameter (v). For the Caldirola-Kanai model, we observe that the flux parameter v decreases the energy dissipation in a quantum dot for a certain range of t.

Revista Brasileira de Ensino de Física•Jan 1, 2021•2 citations

Connecting dissipation and noncommutativity: A Bateman system case study

Sayan Kumar Pal, Partha Nandi, Biswajit Chakraborty

We present an approach to the problem of quantization of the damped harmonic oscillator. To start with, we adopt the standard method of doubling the degrees of freedom of the system (Bateman form) and then, by introducing some new parameters, we get a generalized coupled set of equations from the Bateman form. Using the corresponding time-independent Lagrangian, quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) are analyzed by using both path integral and canonical quantization schemes within the framework of the Hilbert--Schmidt operator formulation. Our method is distinct from those existing in the literature and where the ambient space was taken to be commutative. Our quantization shows that we end up again with a Bateman system except that the damping factor undergoes renormalization. Strikingly, the corresponding expression shows that the renormalized damping factor can be nonzero even if ``bare'' one is zero to begin with. In other words, noncommutativity can act as a source of dissipation. Conversely, the noncommutative parameter $\ensuremath{\theta}$, taken to be a free one now, can be fine tuned to get a vanishing renormalized damping factor. This indicates in some sense a ``duality'' between dissipation and noncommutativity. Our results match the existing results in the commutative limit.

arXiv:1803.03334•Physical Review A•Jun 11, 2018•16 citations
In this work, we investigate a timedependent dissipative scalar field.Inspired by the Bateman lagrangian, we showed a procedure for quantizatizing the massive scalar field with the time-dependent dissipative term.So, the properties of a quantum dissipative scalar field are analyzed by the Caldirola-Kanai model.Also, we construct the Hilbert space for the system and calculate the wave eigen-functions and probability distribution of the system.
The present paper aims at investigating the manner of two dissipative massive scalar fields. Two massive scalar fields that interact with a reservoir were considered and a reservoir was modeled by continuum Klein-Gordon fields. The Lagrangian of the total system was canonically quantized and the dynamics of the system was determined using the Euler-Lagrange equation. Then, the explicit form of the quantum massive scalar fields in long-time limit were observed. The propagator of the system and correlation functions were calculated at finite temperature in the thermofield dynamics formalizem.
Caldirola [Nuovo Cimento 18, 393 (1941)] and Kanai's [Prog. Theor. Phys. 3, 440 (1948)] time-dependent approach for dissipative systems can be traced back to the conventional system-plus-reservoir approach; however, it apparently violates the uncertainty principle. This discrepancy can be avoided by considering a consistent transition between the Caldirola-Kanai formalism and a logarithmic nonlinear Schr\"odinger equation that requires not only a transformation of the operators, but also a nonunitary transformation of the wave function. This procedure also shows the equivalence of three at first sight incompatible approaches to describe dissipative quantum systems.
The problem of the dissipative systems from the quantum point of view has been of increasing interest, but it is far from having a satisfactory solution (1). There are many problems where the dissipation has an important role such as in quantum optics, in quantum analysis of fields, in quantum gravity (2). Dissipation can be observed in interactions between two systems, the observed system and another one often called reservoir or the bath, into which the energy flows via an irreversiblemanner (3). The system is embedded in some environmentwhich is in principle unknown. For an effective description of such systems, we can use time dependent Hamiltonians which in classical physics yield the proper equation of motion. If the friction is a linear funcion of the velocity with friction constant γ the Hamiltonian is the well known Caldirola Kanai Hamiltonian
The harmonic oscillator with time-dependent (indefinite and variable) mass subject to the force proportional to velocity is studied by extending Bateman’s dual Lagrangian and Hamiltonian formalism. To study the quantum analog of such a dissipative system, the Batemann-Morse-Feshback classical Hamiltonian of the damped harmonic oscillator with varying (time-dependent) mass is canonically quantized. In order to discuss the stability of the quantum dissipative system due to the influence of varying mass and the dissipative force, we derived a formula for the vacuum state of the dissipative system with the help of quantum field theoretical framework. It is shown that the formula based on this simple model could be used to study the influence of dissipation such as the instability due to the dissipative force and/or the variable mass. It is understood that the change in the oscillator mass corresponds to a control parameter in quantum dissipative systems.
We analyze the effects of dissipation in a charged oscillator in the presence of the Aharonov-Bohm effect by using time-dependent mass (m(t)) Hamiltonians. We consider two different models for the dissipative Hamiltonian and analyze the uncertainties (Δr and Δp) and the quantum mechanical expectation value of energy (⟨E⟩) in terms of time (t), damping parameters and flux parameter (v). For the Caldirola-Kanai model, we observe that the flux parameter v decreases the energy dissipation in a quantum dot for a certain range of t.
We present an approach to the problem of quantization of the damped harmonic oscillator. To start with, we adopt the standard method of doubling the degrees of freedom of the system (Bateman form) and then, by introducing some new parameters, we get a generalized coupled set of equations from the Bateman form. Using the corresponding time-independent Lagrangian, quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) are analyzed by using both path integral and canonical quantization schemes within the framework of the Hilbert--Schmidt operator formulation. Our method is distinct from those existing in the literature and where the ambient space was taken to be commutative. Our quantization shows that we end up again with a Bateman system except that the damping factor undergoes renormalization. Strikingly, the corresponding expression shows that the renormalized damping factor can be nonzero even if ``bare'' one is zero to begin with. In other words, noncommutativity can act as a source of dissipation. Conversely, the noncommutative parameter $\ensuremath{\theta}$, taken to be a free one now, can be fine tuned to get a vanishing renormalized damping factor. This indicates in some sense a ``duality'' between dissipation and noncommutativity. Our results match the existing results in the commutative limit.