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Nowadays, two of the most prospering fields of physics are quantum computing and spintronics. In both, the loss of information and dissipation plays a crucial role. In the present work we formulate the quantization of the dissipative…
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state…
We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by…
In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…
In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of…
Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational…
The transmission of electric signals on a coupled line with distributed RLC-parameters is considered as a propagation of a dissipative quasi particle. A calculation technique is developed, alternative to the one, accepted for lumped lines.…
We consider the transfer of classical and quantum information through a memory amplitude damping channel. Such a quantum channel is modeled as a damped harmonic oscillator, the interaction between the information carriers - a train of…
Quantum information processing relies on precise control of non-classical states in the presence of many uncontrolled environmental degrees of freedom -- requiring careful orchestration of how the relevant degrees of freedom interact with…
We consider the transfer of quantum information down a single-mode quantum transmission line. Such quantum channel is modeled as a damped harmonic oscillator, the interaction between the information carriers -a train of N qubits- and the…
This work presents results on solutions of the one-dimensional damped wave equation, also called telegrapher's equation, when the initial conditions are general distributions, not only functions. We make a complete deduction of its…
The motivation of this work is to get an additional insight into the irreversible energy dissipation on the quantum level. The presented examination procedure is based on the Feynman path integral method that is applied and widened towards…
In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…
The damped harmonic oscillator is a workhorse for the study of dissipation in quantum mechanics. However, despite its simplicity, this system has given rise to some approximations whose validity and relation to more refined descriptions…
The in-in formalism and its influence functional generalization are widely used to describe the out-of-equilibrium dynamics of unitary and open quantum systems, respectively. In this paper, we build on these techniques to develop an…
We show that the dissipation term in the Hamiltonian for a couple of classical damped-amplified oscillators manifests itself as a geometric phase and is actually responsible for the appearance of the zero point energy in the quantum…
Quantization of the damped harmonic oscillator is taken as leitmotiv to gently introduce elements of quantum probability theory for physicists. To this end, we take (graduate) students in physics as entry level and explain the physical…
The study points out that the traditional solutions to wave equation of dissipative wave and motion equation of block for a multi-degree-of-freedom mass spring damper system are the possible solutions, which are not necessarily objective…
Quantum transmissions of a free particle passing through a rectangular potential barrier with dissipation are studied using a path decomposition technique. Dissipative processes strongly suppress the transmission probability at resonance…
The work considers the damped Pinney equation, defined as the model arising when a linear in velocity damping term is included in the Pinney equation. In the general case the resulting equation does not admit Lie point symmetries or is…