Time operators in stroboscopic wave-packet basis and the time scales in tunneling (original) (raw)
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Time-of-arrival probabilities and quantum measurements: II Application to tunneling times
2007
We formulate quantum tunneling as a time-of-arrival problem: we determine the detection probability for particles passing through a barrier at a detector located a distance L from the tunneling region. For this purpose, we use a Positive-Operator-Valued-Measure (POVM) for the timeof-arrival determined in . This only depends on the initial state, the Hamiltonian and the location of the detector. The POVM above provides a well-defined probability density and an unambiguous interpretation of all quantities involved. We demonstrate that for a class of localized initial states, the detection probability allows for an identification of tunneling time with the classic phase time. We also establish limits to the definability of tunneling time.
Tunneling time through a barrier using the local value of a “time” operator
Physical Review A, 2001
A time for a quantum particle to traverse a barrier is obtained for stationary states by setting the local value of a ''time'' operator equal to a constant. This time operator, called the tempus operator because it is distinct from the time of evolution, is defined as the operator canonically conjugate to the energy operator. The local value of the tempus operator gives a complex time for a particle to traverse a barrier. The method is applied to a particle with a semiclassical wave function, which gives, in the classical limit, the correct classical traversal time. It is also applied to a quantum particle tunneling through a rectangular barrier. The resulting complex tunneling time is compared with complex tunneling times from other methods.
Quantum-shutter approach to tunneling time scales with wave packets
Physical Review A, 2005
The quantum shutter approach to tunneling time scales (G. García-Calderón and A. Rubio, Phys. Rev. A 55, 3361 (1997)), which uses a cutoff plane wave as the initial condition, is extended in such a way that a certain type of wave packet can be used as the initial condition. An analytical expression for the time evolved wave function is derived. The time-domain resonance, the peaked structure of the probability density (as the function of time) at the exit of the barrier, originally found with the cutoff plane wave initial condition, is studied with the wave packet initial conditions. It is found that the time-domain resonance is not very sensitive to the width of the packet when the transmission process is in the tunneling regime.
Quantum temporal probabilities in tunneling systems
Annals of Physics, 2013
In this article, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles, by a careful treatment of temporal observables in quantum theory and through a precise application of the duality between particles and waves. To this end, we employ a new method for constructing probabilities associated to quantum time measurements that provides an explicit link between the tunneling time of particles and the associated quantum fields. We demonstrate that the idea of faster-than-light speeds in tunneling follows from an inadmissible use of classical reasoning in the description of quantum systems. Our results suggest that direct measurements of the transit time in tunneling could provide a new testing ground for the predictions of quantum theory versus local hidden-variables theories.
Relativistic analysis of a wave packet interacting with a quantum-mechanical barrier
Physical Review A, 2003
The dynamics of a wave packet incoming on a quantum-mechanical barrier is analyzed in the framework of a fully relativistic model, with particular emphasis on the case of a large spectrum. Some of the characteristic times of tunneling are calculated and compared; they are all of the same order of magnitude and all indicate an apparent superluminal motion, even if causality is maintained. A time-asymptotic expression for the transmitted wave function is derived and its strong validity is shown.
A Probability Distribution for Quantum Tunneling Times
Advances in High Energy Physics
We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of times for the scattering of a particle through a static rectangular barrier and for the tunneling decay of an initially bound state after the sudden deformation of the potential, the latter case being relevant to understand tunneling times in recent attosecond experiments involving strong field ionization.
Time in Quantum Mechanics and Aspects of the Time-of-Arrival Problem
2014
Time in Quantum Mechanics as a concept and as a measurable quantity is the general topic discussed inside this MSc Dissertation. The inherit difficulty of expressing formally the probabilistic expectation of time measurements via the standard procedure in Quantum Mechanics is explained, focusing specifically on the much studied time-of-arrival problem. Due weight is given in the perception of time measurements in the classical limit and in deriving for reference necessary classical statistical expressions for the timeof-arrival problem. The so called “Pauli’s Theorem” is also explained in detail. While the main focus of the project is on the extensive and detailed presentation of two specific and highly disputable attempts by researchers to construct an apparatus-independent expression for the probability distribution of the time-of-arrival measurements for the free particle case using indeed self-adjoint expressions of operators, an option supposedly prohibited by the “Pauli’s Theo...
Bardon/A Companion to the Philosophy of Time, 2013
First, I briefly review the different conceptions of time held by three rival interpretations of quantum theory: the collapse of the wave-packet, the pilotwave interpretation, and the Everett interpretation (Section 2).
Transmission times of wave packets tunneling through barriers
Journal of Experimental and Theoretical Physics, 1999
The transmission of wave packets through tunneling barriers is studied in detail by the method of quantum molecular dynamics. The distribution function of the times describing the arrival of a tunneling packet in front of and behind a barrier and the momentum distribution function of the packet are calculated. The behavior of the average coordinate of a packet, the average momentum, and their variances is investigated. It is found that under the barrier a part of the packet is reflected and a Gaussian barrier increases the average momentum of the transmitted packet and its variance in momentum space.
Salecker-Wigner-Peres clock and double-barrier tunneling
Physical Review A, 2009
In this work we revisit the Salecker-Wigner-Peres clock formalism and show that it can be directly applied to the phenomenon of tunneling. Then we apply this formalism to the determination of the tunneling time of a non relativistic wavepacket, sharply concentrated around a tunneling energy, incident on a symmetric double barrier potential. In order to deepen the discussion about the generalized Hartmann effect, we consider the case in which the clock runs only when the particle can be found inside the region between the barriers and show that, whenever the probability to find the particle in this region is non negligible, the corresponding time (which in this case turns out to be a dwell time) increases with the barrier spacing.