Related papers: On the Time-Dependent Analysis of Gamow Decay
Gamow's approach to exponential decay of meta-stable particles via complex 'eigenvalues' (resonances) of a Hamiltonian is scrutinized. We explain the sense in which the non-square-integrable 'eigenfunctions' that belong to these resonances…
For single-particle nonrelativistic quantum mechanics, a Gamow state is an eigenfunction of the Hamiltonian with complex eigenvalue. Gamow states are not normalizable; they depend on time via the usual multiplier exp(-iEt) supplemented by a…
We present a theoretical analysis of quantum decay in which the survival probability is replaced by a decay rate that is equal to the absolute value squared of the wave function in the time representation. The wave function in the time…
We examine Gamow's method for calculating the decay rate of a wave function initially located within a potential well. Using elementary techniques, we examine a very simple, exactly solvable model, in order to show why it is so reliable for…
Decaying states can be represented by Gamow vectors with an exponential, asymmetric time evolution. This asymmetric evolution is a manifestation of irreversibility on the microphysical level. The Rigged Hilbert Space provides a mathematical…
Gamow vectors have been developed in order to give a mathematical description for quantum decay phenomena. Mainly, they have been applied to radioactive phenomena, scattering and to some decoherence models. They play a crucial role in the…
By using the fact that the Gamow states in the momentum representation are square integrable, we obtain the differential and the total decay width of a two-body, non-relativistic decay. The resulting Gamow Golden Rule is well suited to…
We obtain the precise form of two Gamow functionals, representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing…
Though the classical treatment of spontaneous decay leads to an exponential decay law, it is well known that this is an approximation of the quantum mechanical result which is a non-exponential at very small and large times for narrow…
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature od the quantum decay process is the presence of three time regimes of the decay process: the early time…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: indeed, the decay is initially quadratic, while at very large times…
By using an exact analytical non-Hermitian approach in terms of resonance (quasinormal) states we express the decaying wave function as the sum of exponential and nonexponential decaying solutions to the time-dependent Schr\"odinger…
We study the time evolution of two wave packets prepared at the same initial state, but evolving under slightly different Hamiltonians. For chaotic systems, we determine the circumstances that lead to an exponential decay with time of the…
A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also…
The quantum mechanical approach developed by us recently for the evolution of the universe is used to derive an alternative derivation connecting the temperature of the cosmic background radiation and the age of the universe which is found…
The Gamow vector description of resonances is compared with the S-matrix and the Green function descriptions using the example of the square barrier potential. By imposing different boundary conditions on the time independent Schrodinger…
The method developed by Van Dijk, Nogami and Toyama for obtaining the time-evolved wave function of a decaying quantum system is generalized to potentials and initial wave functions of non-compact support. The long time asymptotic behavior…
A fundamental aspect of the quantum-to-classical limit is the transition from a non-commutative algebra of observables to commutative one. However, this transition is not possible if we only consider unitary evolutions. One way to describe…