Related papers: Quantum Instantons and Quantum Chaos
We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths…
The notion of quantum information related to the two different perspectives of the global and local states is examined. There is circularity in the definition of quantum information because we can speak only of the information of systems…
Quantum phase transitions encompass a variety of phenomena that occur in quantum systems exhibiting several possible symmetries. Traditionally, these transitions are explored by continuously varying a control parameter that connects two…
Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized…
Some models allowing explicit calculation of periodic instantons and evaluation of their action are studied with regard to transitions from classical to quantum behaviour as the temperature is lowered and tunneling sets in. It is shown that…
It is well known that a quantum circuit on $N$ qubits composed of Clifford gates with the addition of $k$ non Clifford gates can be simulated on a classical computer by an algorithm scaling as $\text{poly}(N)\exp(k)$[1]. We show that, for a…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
The agenda of Dissipative Quantum Chaos is to create a toolbox which would allow us to categorize open quantum systems into "chaotic" and "regular" ones. Two approaches to this categorization have been proposed recently. One of them is…
We discuss the necessity and demonstrate the validity of introduction the notion of deterministic chaos in quantum field theory. Brief review of the existing approaches to this problem is given. We compare proposed chaos criterion for…
We treat the double well quantum oscillator from the standpoint of the Ehrenfest equation but in a manner different from Pattanayak and Schieve. We show that for short times there can be chaotic motion due to quantum fluctuations, but over…
The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates which are characterized by quantized vorticity, uperfluidity and, at finite temperatures,…
We review the theory and phenomenology of instantons in QCD. After a general overview, we provide a pedagogical introduction to semi-classical methods in quantum mechanics and field theory. The main part of the review summarizes our…
A new instanton solution is found in the quantum-mechanical double-well potential with a four-fermion term. The solution has finite action and depends on four fermionic collective coordinates. We explain why in general the instanton action…
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum…
We propose the necessary and sufficient condition for the presence of quantum entanglement in arbitrary symmetric pure states of two-level atomic systems. We introduce a parameter to quantify quantum entanglement in such systems. We express…
Processes leading to anomalous fluctuations in turbulent flows, referred to as intermittency, are still challenging. We consider cascade trajectories through scales as realizations of a stochastic Langevin process for which multiplicative…
Entanglement is not only the most intriguing feature of quantum mechanics, but also a key resource in quantum information science. The entanglement content of random pure quantum states is almost maximal; such states find applications in…
We discuss the quantisation of a class of string cosmology models that are characterized by scale factor duality invariance. We compute the amplitudes for the full set of classically allowed and forbidden transitions by applying the reduce…
The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several…
The energy levels of the double-well potential receive, beyond perturbation theory, contributions which are non-analytic in the coupling strength; these are related to instanton effects. For example, the separation between the energies of…