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States prepared by decay

Stig Stenholm, Asta Paloviita

Published Jan 1, 1997• 2 citations
OpenAlex

Abstract

We consider the time evolution of a discrete state embedded in a continuum. Results from scattering theory can be utilized to solve the initial value problem and discuss the system as a model of wave packet preparation. Extensive use is made of the analytic properties of the propagators, and simple model systems are evaluated to illustrate the argument. We verify the exponential appearence of the continuum state and its propagation as a localized wave packet.

Related papers

States prepared by decay

Stig Stenholm, Asta Paloviita

We consider the time evolution of a discrete state embedded in a continuum. Results from scattering theory can be utilized to solve the initial value problem and to discuss the system as a model of wave packet preparation. Extensive use is made of the analytic properties of the propagators, and simple model systems are evaluated to illustrate the argument. We verify the exponential appearence of the continuum state and its propagation as a localized wave packet.

Journal of Modern Optics•Nov 1, 1997•0 citations

States prepared by decay

Stig Stenholm, Asta Paloviita

We consider the time evolution of a discrete state embedded in a continuum. Results from scattering theory can be utilized to solve the initial value problem and to discuss the system as a model of wave packet preparation. Extensive use is made of the analytic properties of the propagators, and simple model systems are evaluated to illustrate the argument. We verify the exponential appearence of the continuum state and its propagation as a localized wave packet.

arXiv:quant-ph/9702059•Journal of Modern Optics•Nov 1, 1997•4 citations

Unified analytical description of the time evolution of decay for initial states formed by wave-packet scattering and by initial decaying states in quantum systems

Sergio Cordero, Gastón García‐Calderón, Roberto Romo +1 more

We consider a unified analytical approach for scattering and decay processes in one-dimensional resonant tunneling systems using the formalism of resonant states to address the issue of the differences and similarities in the time evolution of decay between the decay of an arbitrary state prepared initially within a system and the formation and subsequent decay of a quasistationary state in the scattering of a Gaussian wavepacket on that system. We find three distinctive regimes. A first regime, which refers only to the quasistationary state, that is characterized by a buildup time of the probability density at a given position within the internal region of the potential. Here we find that the buildup time has a dependence on position. A second regime, dominated by the exponentially decaying terms, where the decay of the quasistationary state proceeds in an almost identical fashion as for the initially prepared decaying state. And finally, a third regime that involves the transition to nonexponential decay at long times and its ulterior behavior as an inverse power of time. Here we find that the time scale of the transition occurs at different times, which implies a dependence on the parameters of the initial state.

Physical Review A•Oct 24, 2011•15 citations

Wave-packet Dynamics in Unconventional RMT Models

James Aisenberg

We analyze the wave-packet dynamics scenario produced by Random Matrix Theory models with unconventional band-profile structures. Our motivation is to understand the energy spreading of quantum systems with complex dynamics. Examples of such systems include complex nuclei, atoms and molecules, quantum dots, and Bose-Einstein Condensates in optical traps, which, under the influence of an external perturbation, experience an energy redistribution of the initially prepared state. Such a perturbation could be due to an external electric or magnetic field, a change in the confining geometry, or a residual interaction, among other things. Of special interest in our analysis is the investigation of the time relaxation properties of a prepared state into a sea of other states (the continuum). We find that, for a large family of power spectra characterized by a non-flat profile, the survival probability $P(t)$ might exhibit either exponential-like or power-law decay.

•Jan 1, 2009•0 citations

Time Arrow in Wave-Packet Evolution

R. Englman, Asher Yahalom A

Availability of short, femtosecond laser pulses has recently made feasible the probing of phases in an atomic or molecular wave-packet (superposition of energy eigenstates). With short duration excitations the initial form of the wave-packet is an essentially real "doorway state", and this develops phases for each of its component amplitudes as it evolves. It is suggested that these phases are hallmarks of a time arrow and irreversibility that are inherent in the quantum mechanical processes of preparation and evolution. To display the non-triviality of the result, we show under what conditions it would not hold; to discuss its truth, we consider some apparent contradictions. We propose that (in time-reversal invariant systems) the preparation of "initially" complex wave-packets needs finite times to complete, i.e., is not instantaneous.

arXiv:cond-mat/0007142•Jul 9, 2000•0 citations

An exponential two-state model for collisional excitation via a continuum

Victor Sidis, Danielle Grimbert, C Courbin

The authors consider a new case of collision-induced transitions between two discrete (quasistationary) states embedded in a continuum. The energy difference ( delta =E 1 -E 2 ) between the two states is assumed to remain constant throughout the collision whereas the difference between their individual decay widths ( Gamma 1 - Gamma 2 ) and their imaginary couplings (iV 1,2 ) via the continuum have a common exponential dependence: (E 1 -i Gamma 1 /2)-(E 2 -i Gamma 2 /2)= delta -ig exp(- eta R) iV 1,2 =iF 1,2 exp(- eta R). Transition probabilities are determined in closed analytical form for this problem.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 28, 1988•6 citations
We consider the time evolution of a discrete state embedded in a continuum. Results from scattering theory can be utilized to solve the initial value problem and discuss the system as a model of wave packet preparation. Extensive use is made of the analytic properties of the propagators, and simple model systems are evaluated to illustrate the argument. We verify the exponential appearence of the continuum state and its propagation as a localized wave packet.
We consider a unified analytical approach for scattering and decay processes in one-dimensional resonant tunneling systems using the formalism of resonant states to address the issue of the differences and similarities in the time evolution of decay between the decay of an arbitrary state prepared initially within a system and the formation and subsequent decay of a quasistationary state in the scattering of a Gaussian wavepacket on that system. We find three distinctive regimes. A first regime, which refers only to the quasistationary state, that is characterized by a buildup time of the probability density at a given position within the internal region of the potential. Here we find that the buildup time has a dependence on position. A second regime, dominated by the exponentially decaying terms, where the decay of the quasistationary state proceeds in an almost identical fashion as for the initially prepared decaying state. And finally, a third regime that involves the transition to nonexponential decay at long times and its ulterior behavior as an inverse power of time. Here we find that the time scale of the transition occurs at different times, which implies a dependence on the parameters of the initial state.
We analyze the wave-packet dynamics scenario produced by Random Matrix Theory models with unconventional band-profile structures. Our motivation is to understand the energy spreading of quantum systems with complex dynamics. Examples of such systems include complex nuclei, atoms and molecules, quantum dots, and Bose-Einstein Condensates in optical traps, which, under the influence of an external perturbation, experience an energy redistribution of the initially prepared state. Such a perturbation could be due to an external electric or magnetic field, a change in the confining geometry, or a residual interaction, among other things. Of special interest in our analysis is the investigation of the time relaxation properties of a prepared state into a sea of other states (the continuum). We find that, for a large family of power spectra characterized by a non-flat profile, the survival probability P(t)P(t)P(t) might exhibit either exponential-like or power-law decay.
Availability of short, femtosecond laser pulses has recently made feasible the probing of phases in an atomic or molecular wave-packet (superposition of energy eigenstates). With short duration excitations the initial form of the wave-packet is an essentially real "doorway state", and this develops phases for each of its component amplitudes as it evolves. It is suggested that these phases are hallmarks of a time arrow and irreversibility that are inherent in the quantum mechanical processes of preparation and evolution. To display the non-triviality of the result, we show under what conditions it would not hold; to discuss its truth, we consider some apparent contradictions. We propose that (in time-reversal invariant systems) the preparation of "initially" complex wave-packets needs finite times to complete, i.e., is not instantaneous.
The authors consider a new case of collision-induced transitions between two discrete (quasistationary) states embedded in a continuum. The energy difference ( delta =E 1 -E 2 ) between the two states is assumed to remain constant throughout the collision whereas the difference between their individual decay widths ( Gamma 1 - Gamma 2 ) and their imaginary couplings (iV 1,2 ) via the continuum have a common exponential dependence: (E 1 -i Gamma 1 /2)-(E 2 -i Gamma 2 /2)= delta -ig exp(- eta R) iV 1,2 =iF 1,2 exp(- eta R). Transition probabilities are determined in closed analytical form for this problem.