Related papers: Forbidden trajectories for path integrals
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last ten years or so, including, of course, the main…
The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…
Majorana fermions are currently of huge interest in the context of nanoscience and condensed matter physics. Different to usual fermions, Majorana fermions have the property that the particle is its own anti-particle thus, they must be…
we will show the existence and uniqueness of a real-time, time-sliced Feynman path integral for quantum systems with vector potential. Our formulation of the path integral will be derived on the $L^2$ transition probability amplitude via…
A semiclassical method of complex trajectories for the calculation of the tunneling exponent in systems with many degrees of freedom is further developed. It is supplemented with an easily implementable technique, which enables one to…
We calculate the excitonic optical absorption spectra of (In,Ga)As/GaAs self-assembled quantum dots by adopting an atomistic pseudopotential approach to the single-particle problem followed by a configuration-interaction approach to the…
A review of discrete quantum walk with two particle is given. The use of different states encountered in identical particle, and the idea of entanglement and superposition is explored to explored the interesting dynamics of two particle…
The proposal that the one-parameter solutions of the real part of the Schrodinger equation (quantum Hamilton-Jacobi equation) can be regarded as `quantum particle trajectories' has received considerable attention recently. Opinions as to…
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
Quantum tunneling is mostly discussed in the Euclidean path integral formalism using instantons. On the other hand, it is difficult to understand quantum tunneling based on the real-time path integral due to its oscillatory nature, which…
For a connected graph, a path containing all vertices is known as \emph{Hamiltonian path}. For general graphs, there is no known necessary and sufficient condition for the existence of Hamiltonian paths and the complexity of finding a…
A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of $C^\alpha$, by only allowing paths which possess at least $\alpha$ derivatives. The method introduces two external…
We revisit the minimum-link path problem: Given a polyhedral domain and two points in it, connect the points by a polygonal path with minimum number of edges. We consider settings where the vertices and/or the edges of the path are…
The path integral of four dimensional quantum gravity is restricted to conformally self-dual metrics. It reduces to integrals over the conformal factor and over the moduli space of conformally self--dual metrics and can be studied with the…
Quantum theory permits interference between indistinguishable paths but, at the same time, restricts its order. Single-particle interference, for instance, is limited to the second order, that is, to pairs of single-particle paths. To date,…
We theoretically investigate resonant tunneling through a linear array of quantum dots with subsequent tunnel coupling. We consider two limiting cases: (i) strong Coulomb blockade, where only one extra electron can be present in the array…
In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic…
We describe a quantum particle constrained on a catenoid, employing an effective description of quantum mechanics based on expected values of observables and quantum dispersions. We obtain semiclassical trajectories for particles,…