Related papers: The Arbitrary Trajectory Quantization Method
The article contains an overview of authors achievements in development of alternative quantum-chemical approaches oriented towards revival of the classical tradition of qualitative chemical thinking instead of obtaining numerical results.…
The Quantum Trajectories Method (QTM) is one of {the} frequently used methods for studying open quantum systems. { The main idea of this method is {the} evolution of wave functions which {describe the system (as functions of time). Then,}…
Closed orbit theory is generalized to the semiclassical calculation of cross-correlated recurrence functions for atoms in external fields. The cross-correlation functions are inverted by a high resolution spectral analyzer to obtain the…
Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using the adiabatic condition. The adiabatic condition consists of two parts: an energy gap and a transition…
The quantum baker's map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study…
Quantum systems in specific regimes display recurrences at the period of the periodic orbits of the corresponding classical system. We investigate the excited hydrogen atom in a magnetic field -- a prototypical system of 'quantum chaos' --…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters.…
An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling…
This paper deals with the classical trajectories for two super-integrable systems: a system known in quantum chemistry as the Hartmann system and a system of potential use in quantum chemistry and nuclear physics. Both systems correspond to…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
Quantization of the parameters of machine learning models, such as deep neural networks, requires solving constrained optimization problems, where the constraint set is formed by the Cartesian product of many simple discrete sets. For such…
Gutzwiller's trace formula has a central place in quantum chaos because it provides semiclassical approximations for quantum energy levels in classically chaotic systems by linking them to classical periodic orbits. In this didactic…
The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system.…
The Gutzwiller trace formula provides a semiclassical approximation for the density of states of a quantum system in terms of classical periodic orbits. In its original form Gutzwiller derived the trace formula for quantum systems without…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…
To study electronic transport through chaotic quantum dots, there are two main theoretical approachs. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other…
We derive the semiclassical WKB quantization condition for obtaining the energy band edges of periodic potentials. The derivation is based on an approach which is much simpler than the usual method of interpolating with linear potentials in…
To assess whether a gate-based quantum algorithm can be executed successfully on a noisy intermediate-scale quantum (NISQ) device, both complexity and actual value of quantum resources should be considered carefully. Based on quantum phase…
We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or…