A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi-bound (or resonance) states. When the system is prepared in one of such quasi-bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and due to quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers.
A quantum particle constrained between two high potential barriers provides a paradigmatic example of a system sustaining quasi-bound (or resonance) states. When the system is prepared in one of such quasi-bound states, the wave function approximately maintains its shape but decays in time in a nearly exponential manner radiating into the surrounding space, the lifetime being of the order of the reciprocal of the width of the resonance peak in the transmission spectrum. Naively, one could think that adding more lateral barriers would preferentially slow down or prevent the quantum decay since tunneling is expected to become less probable and due to quantum backflow induced by multiple scattering processes. However, this is not always the case and in the early stage of the dynamics quantum decay can be accelerated (rather than decelerated) by additional lateral barriers, even when the barrier heights are arbitrarily large. The decay acceleration originates from resonant tunneling effects and is associated to large deviations from an exponential decay law. We discuss such a counterintuitive phenomenon by considering the hopping dynamics of a quantum particle on a tight-binding lattice with on-site potential barriers.
We examine a fast decay process that arises in the transition period between the Gaussian and exponential decay processes in quantum decay systems. It is usually expected that the decay is decelerated by a confinement potential barrier. However, we find a case where the decay in the transition period is accelerated by tunneling through a confinement potential barrier. We show that the acceleration gives rise to an appreciable effect on the time evolution of the nonescape probability of the decay system.
The most unstable quantum states and elementary particles possess more than a single decay channel. At the same time, it is well known that typically the decay law is not simply exponential. Therefore, it is natural to ask how to spot the nonexponential decay when (at least) two decay channels are opened. In this work, we study the tunneling phenomenon of an initially localized particle in two spatially opposite directions through two different barriers, mimicking two decay channels. In this framework, through specific quantum mechanical examples which can be accurately solved, we study the general properties of a two-channel decay that apply for various unstable quantum states (including unstable particles). Apart from small deviations at early times, the survival probability and the partial tunneling probability along the chosen direction are very well described by the exponential-decay model. In contrast, the ratios of the decay probabilities and probability currents are evidently not a simple constant (as they would be in the exponential limit), but display time-persisting oscillations. Hence, these ratios are optimal witnesses of deviations from the exponential-decay law.
Abstract Quantum tunneling through potential barriers plays a central role in diverse physical phenomena ranging from nuclear fusion and radioactive decay to semiconductor devices and superconducting technologies. In this work, we calculate tunneling probabilities and wave functions for an arbitrary number of potential barriers with diverse functional forms, including square, Gaussian, parabolic, and Lorentzian profiles, using a general numerical framework. The numerical results are first validated by comparison with exact analytical solutions for double, triple and quadruple-square barrier systems, demonstrating excellent agreement. The results reveal that for a system with N barriers, a single resonance peak splits into ( N − 1 ) distinct peaks, which eventually merge into an energy band as N becomes large, in a manner fully consistent with the existing literature. A key additional result is the incorporation of absorption effects through an imaginary component of the potential, providing a realistic description of particle trapping and leading to a progressive suppression of resonant transmission. For sufficiently strong absorption, the resonant structures are completely washed out. Further, if the barriers become non-uniform or disordered, the regular resonance pattern is also observed to be completely washed out. These findings demonstrate the broad applicability of the approach to complex potential landscapes and offer insights relevant to both fundamental quantum mechanics and the design of next-generation quantum devices.
We examine a one-dimensional model of a decaying quantum system, e.g., one that could simulate decay. A particle is initially confined in a region and leaks out, tunnelling through a potential barrier. The same model has been examined before, primarily to study decay properties which are determined by the wavefunction of the particle within the potential barrier. However, the wavefunction of this model (and of any similar models) outside the potential barrier has not been obtained explicitly as a function of position and time. We obtain the wavefunction outside as well as inside the potential barrier by solving the time-dependent Schrödinger equation, and explore various features of the space-time development of the system. In an early study by Winter it was pointed out that the probability current just outside the barrier, after a long time, may fluctuate and can be negative, i.e., inward. We find that under certain circumstances the amplitude of the fluctuations increases significantly as the distance from the barrier increases. We propose a simple approximate wavefunction that works well when the decay is very slow. The Gamow wavefunction, commonly used to describe the -decay process, is not appropriate at large distances. Our wavefunction can be used anywhere and is normalized in the usual manner.
Recently we outlined an analytical method of solving the time-dependent Schr\"odinger equation for a model which simulates a decaying quantum system such as an $\ensuremath{\alpha}$-decaying nucleus. A particle in the model is initially confined around the origin and leaks out, tunneling through a potential barrier. The solution can be expressed as a linear combination of the Moshinsky functions, each of which is associated with a pole of the scattering S matrix of the model. In this paper we give a full account of the method with a few explicit examples. We examine deviations from the exponential decay law at very large times. We comment on a recent controversy regarding the t dependence of the survival and nonescape probabilities when t is very large.
While exponential decay is ubiquitous in nature, deviations at both short and long times are dictated by quantum mechanics. Nonexponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying products. We discuss the quantum decay dynamics by tunneling of a many-particle system, characterizing the long-time nonexponential behavior of the nonescape and survival probabilities. The effects of contact interactions and quantum statistics are described. It is found that, whereas for noninteracting bosons the long-time decay follows a power law with an exponent linear in the number of particles N, the exponent becomes quadratic in N in the fermionic case. The same results apply to strongly interacting many-body systems related by the generalized Bose-Fermi duality. The faster fermionic decay can be traced back to the effective hard-core interactions between particles, which are as well the decaying products, and exhibit spatial antibunching which hinders the reconstruction of the initial unstable state. The results are illustrated with a paradigmatic model of quantum decay from a trap allowing leaks by tunneling, whose dynamics is described exactly by means of an expansion in resonant states.