Fractional quantum mechanics of open quantum systems
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Vasily E. Tarasov
Abstract
Fractional dynamics of open quantum systems with power-law memory is described. We show that the quantum processes can demonstrate a universal dynamic behavior caused by the effects of power-law fading memory. We propose generalizations of time-ordered exponential and time-ordered product for processes with powerlaw memory. As examples, we consider equations of the N-level open quantum system with memory, quantum oscillator with friction and memory. The solutions of the corresponding fractional differential equations with derivatives of noninteger orders are obtained.
Abstract
Fractional dynamics of open quantum systems with power-law memory is described. We show that the quantum processes can demonstrate a universal dynamic behavior caused by the effects of power-law fading memory. We propose generalizations of time-ordered exponential and time-ordered product for processes with powerlaw memory. As examples, we consider equations of the N-level open quantum system with memory, quantum oscillator with friction and memory. The solutions of the corresponding fractional differential equations with derivatives of noninteger orders are obtained.
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Fractional electromagnetics 1
- Fractional electrodynamics with spatial dispersion 25
- Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics 53
- Fractional diffusion-wave phenomena 71
- Fractional diffusion and parametric subordination 99
- The fractional advection-dispersion equation for contaminant transport 129
- Anomalous diffusion in interstellar medium 151
- Fractional kinetics in random/complex media 183
- Nonlocal quantum mechanics: fractional calculus approach 207
- Fractional quantum fields 237
- Fractional quantum mechanics of open quantum systems 257
- Fractional quantum mechanics with topological constraint 279
- Fractional time quantum mechanics 299
- Index 317
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Fractional electromagnetics 1
- Fractional electrodynamics with spatial dispersion 25
- Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics 53
- Fractional diffusion-wave phenomena 71
- Fractional diffusion and parametric subordination 99
- The fractional advection-dispersion equation for contaminant transport 129
- Anomalous diffusion in interstellar medium 151
- Fractional kinetics in random/complex media 183
- Nonlocal quantum mechanics: fractional calculus approach 207
- Fractional quantum fields 237
- Fractional quantum mechanics of open quantum systems 257
- Fractional quantum mechanics with topological constraint 279
- Fractional time quantum mechanics 299
- Index 317
