187 research outputs found
Exactly solvable time-dependent models of two interacting two-level systems
Two coupled two-level systems placed under external time-dependent magnetic
fields are modeled by a general Hamiltonian endowed with a symmetry that
enables us to reduce the total dynamics into two independent two-dimensional
sub-dynamics. Each of the sub-dynamics is shown to be brought into an exactly
solvable form by appropriately engineering the magnetic fields and thus we
obtain an exact time evolution of the compound system. Several physically
relevant and interesting quantities are evaluated exactly to disclose
intriguing phenomena in such a system.Comment: 15 pages, 13 figure
Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields
The quantum dynamics of a
-conserving
Hamiltonian model describing two coupled spins and
under controllable and fluctuating time-dependent magnetic
fields is investigated. Each eigenspace of is dynamically
invariant and the Hamiltonian of the total system restricted to any one of such
eigenspaces, possesses the SU(2) structure of the
Hamiltonian of a single fictitious spin acted upon by the total magnetic field.
We show that such a reducibility holds regardless of the time dependence of the
externally applied field as well as of the statistical properties of the noise,
here represented as a classical fluctuating magnetic field. The time evolution
of the joint transition probabilities of the two spins and
between two prefixed factorized states is examined,
bringing to light peculiar dynamical properties of the system under scrutiny.
When the noise-induced non-unitary dynamics of the two coupled spins is
properly taken into account, analytical expressions for the joint Landau-Zener
transition probabilities are reported. The possibility of extending the
applicability of our results to other time-dependent spin models is pointed
out.Comment: 11 pages, 5 figure
An example of interplay between Physics and Mathematics: Exact resolution of a new class of Riccati Equations
A novel recipe for exactly solving in finite terms a class of special
differential Riccati equations is reported. Our procedure is entirely based on
a successful resolution strategy quite recently applied to quantum dynamical
time-dependent SU(2) problems. The general integral of exemplary differential
Riccati equations, not previously considered in the specialized literature, is
explicitly determined to illustrate both mathematical usefulness and easiness
of applicability of our proposed treatment. The possibility of exploiting the
general integral of a given differential Riccati equation to solve an SU(2)
quantum dynamical problem, is succinctly pointed out.Comment: 10 page
Spin-1/2 sub-dynamics nested in the quantum dynamics of two coupled qutrits
In this paper we investigate the quantum dynamics of two spin-1 systems,
and , adopting a generalized
-nonconserving Heisenberg model. We
show that, due to its symmetry property, the nine-dimensional dynamics of the
two qutrits exactly decouples into the direct sum of two sub-dynamics living in
two orthogonal four- and five-dimensional subspaces. Such a reduction is
further strengthened by our central result consisting in the fact that in the
four-dimensional dynamically invariant subspace, the two qutrits quantum
dynamics, with no approximations, is equivalent to that of two non interacting
spin 1/2's. The interpretative advantages stemming from such a remarkable and
non-intuitive nesting are systematically exploited and various intriguing
features consequently emerging in the dynamics of the two qutrits are deeply
scrutinised. The possibility of exploiting the dynamical reduction brought to
light in this paper for exactly treating as well time-dependent versions of our
Hamiltonian model is briefly discussed.Comment: 14 pages, 11 figures; Last two authors name corrected, corrected
typos, Fig. 11 changed (same result
Stochastic 0-dimensional Biogeochemical Flux Model: Effect of temperature fluctuations on the dynamics of the biogeochemical properties in a marine ecosystem
We present a new stochastic model, based on a 0-dimensional version of the well known biogeochemical flux model (BFM), which allows to take into account the temperature random fluctuations present in natural systems and therefore to describe more realistically the dynamics of real marine ecosystems. The study presents a detailed analysis of the effects of randomly varying temperature on the lower trophic levels of the food web and ocean biogeochemical processes. More in detail, the temperature is described as a stochastic process driven by an additive self-correlated Gaussian noise. Varying both correlation time and intensity of the noise source, the predominance of different plankton populations is observed, with regimes shifted towards the coexistence or the exclusion of some populations. Finally a Fourier analysis carried out on the time series of the plankton populations shows how the ecosystem responds to the seasonal driving for different values of the noise intensit
Dzyaloshinskii-Moriya and dipole-dipole interactions affect coupling-based Landau-Majorana-Stückelberg-Zener transitions
It has been theoretically demonstrated that two spins (qubits or qutrits), coupled by exchange interaction only, undergo a coupling-based joint Landau-Majorana-Stuckelberg-Zener (LMSZ) transition when a linear ramp acts on one of the two spins. Such a transition, under appropriate conditions on the parameters, drives the two-spin system toward a maximally entangled state. In this paper, effects on the quantum dynamics of the two qudits, stemming from the Dzyaloshinskii-Moriya (DM) and dipole-dipole (d-d) interactions, are investigated qualitatively and quantitatively. The enriched Hamiltonian model of the two spins shares with the previous microscopic one the same C2 symmetry which once more brings about an exact treatment of the new quantum dynamical problem. This paper transparently reveals that the DM and d-d interactions generate independent, enhancing or hindering, modifications in the dynamical behavior predicted for the two spins coupled exclusively by the exchange interaction. It is worthwhile to notice that, on the basis of the theory here developed, the measurement of the time evolution of the magnetization in a controlled LMSZ scenario can furnish information on the relative weights of the three kinds of couplings describing the spin system. This possibility is very important since it allows us in principle to legitimate the choice of the microscopic model to be adopted in a given physical scenario
Characterization of Quantum and Classical Critical Points for an Integrable Two-Qubit Spin-Boson Model
The class of two-interacting-qubit spin-boson models with vanishing transverse fields on the spin-pair is studied. The model can be mapped exactly into two independent standard single-impurity spin-boson models where the role of the tunneling parameter is played by the spin-spin coupling. The dynamics of the magnetization are analyzed for different levels of (an)isotropy. The existence of a decoherence-free subspace, as well as of different classical regimes separated by a critical temperature, and symptoms of quantum (first-order and Kosterlitz-Thouless type) phase transitions in the Ohmic regime are brought to light
Coupled quantum pendula as a possible model for Josephson-junction-based axion detection
The model of two coupled quantum pendula is studied and its suitability to describe Josephson junctions interacting with axions is analysed. It is shown that some physical features of one pendulum, not directly accessible, can be deduced by local measures on the other one, which is experimentally available. Such an effect can be exploited for the axion (the invisible pendulum) detection based on Josephson junctions (the accessible pendulum). The interaction between axion and Josephson junction can be enhanced at the resonance, if the axion and the junction frequencies match, and if the accessible system is prepared in the most convenient initial quantum state
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