Search Results (155)

We investigate the quantum dynamics of coherence in the hyperfine structure of hydrogen atoms subjected to dephasing noise, modeled using the Lindblad master equation. The effective Hamiltonian describes the spin–spin interaction between the electron and proton, with dephasing introduced via Lindblad operators. Analytical solutions for the time-dependent density matrix are derived for various initial states, including separable, partially entangled, and maximally entangled configurations. Quantum coherence is quantified through the $l_1$-norm measures, while purity is evaluated to assess mixedness. Results demonstrate that coherence exhibits oscillatory decay modulated by the dephasing rate, with antiparallel spin states showing greater resilience against noise compared to parallel configurations. These findings highlight the interplay between coherent hyperfine dynamics and environmental dephasing, offering insights into preserving quantum resources in atomic systems for applications in quantum information science. Full article

Spin waves represent an important class of low-energy excitations in magnetic solids, which influence the thermodynamic properties and play a major role in technical applications, such as spintronics or magnetic data storage. Despite the enormous advances of ab initio simulations in materials science, quantitative calculations of spin-wave spectra still pose a significant challenge, because the collective nature of the spin dynamics requires an accurate treatment of the Coulomb interaction between the electrons. As a consequence, simple lattice models like the Heisenberg Hamiltonian are still widespread in practical investigations, but modern techniques like time-dependent density-functional theory or many-body perturbation theory also open a route to material-specific spin-wave calculations from first principles. Although both are in principle exact, actual implementations necessarily employ approximations for electronic exchange and correlation as well as additional numerical simplifications. In this review, we recapitulate the theoretical foundations of ab initio spin-wave calculations and analyze the common approximations that underlie present implementations. In addition, we survey the available results for spin-wave dispersions of various magnetic materials and compare the performance of different computational approaches. In this way, we provide an overview of the present state of the art and identify directions for further developments. Full article

We analyzed the accuracy of digitized adiabatic quantum computing to form the entangled three-qubit Greenberger–Horne–Zeilinger (GHZ) state on two IBM quantum computers and four quantum simulators by comparison with direct calculations using a Python code (version 3.12). We initialized three-qubit systems in the ground state of the Hamiltonian for noninteracting spins in an applied magnetic field in the x direction. We then gradually varied the Hamiltonian to an Ising model form with nearest-neighbor zz spin coupling with an eight-step discretization. The von Neumann entropy provides an indicator of the accuracy of the discretized adiabatic evolution. The von Neumann entropy of the density matrix from the Python code remains very close to zero, while the von Neumann entropy of the density matrices on the quantum computers increases almost linearly with the step number in the process. The GHZ witness operator indicates that the quantum simulators incorporate a GHZ component in part. The states on the two quantum computers acquire partial GHZ character, even though the trace of the product of the GHZ witness operator with the density matrix not only remains positive but also rises monotonically from Step 5 to Step 8. Each of the qubits becomes entangled during the adiabatic evolution in all of the calculations, as shown by the single-qubit reduced density matrices. Full article

In this work, we investigate the quantum coherence and purity in hydrogen atoms under dissipative dynamics, with a focus on the hyperfine structure states arising from the electron–proton spin interaction. Using the Lindblad master equation, we model the time evolution of the density matrix of the system, incorporating both the unitary dynamics driven by the hyperfine Hamiltonian and the dissipative effects due to environmental interactions. Quantum coherence is quantified using the $L_1$ norm and relative entropy measures, while purity is assessed via von Neumann entropy, for initial states, including a maximally entangled Bell state and a separable state. Our results reveal distinct dynamics: for the Bell states, both coherence and purity decay exponentially with a rate proportional to the dissipation parameter, whereas for a kind of separable state, coherence exhibits oscillatory behavior modulated via the hyperfine coupling constant, superimposed on an exponential decay, and accompanied by a steady increase in entropy. Higher dissipation rates accelerate the loss of coherence and the growth of von Neumann entropy, underscoring the environment’s role in suppressing quantum superposition and driving the system towards mixed states. These findings enhance our understanding of coherence and purity preservation in atomic systems and offer insights for quantum information applications where robustness against dissipation is critical. Full article

We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior, raising the question of whether a measure of complexity can track this process. In addition to examining observable equilibration, we extend our analysis to study how the complexity of the quantum states evolves, providing insight into the transition from initial coherence to equilibrium. We define a classical statistical complexity measure based on observable entropy and deviation from equilibrium, which captures the dynamical progression towards equilibration and effectively distinguishes between complex and non-complex trajectories. In particular, our measure is sensitive to non-complex dynamics. Such dynamics include the quasi-periodic behavior exhibited by low-dimensional initial states, where the system explores a limited region of Hilbert space while preserving coherence. Numerical simulations of an Ising-like non-integrable Hamiltonian spin-chain model support these findings. Our work provides new insight into the emergence of equilibrium behavior from unitary dynamics and advances complexity as a meaningful tool in the study of the emergence of classicality in microscopic systems. Full article

We present an economical approach to treat spin–orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian is then augmented with the Breit–Pauli Hamiltonian and diagonalized using spin-pure reference states to obtain the SOC-corrected energy spectrum. The spin–orbit mean-field approximation is also assumed to reduce the cost associated with the two-electron spin–orbit integrals. The resulting method is termed BP1-SA-DSRG-PT2c, and it possesses the same computational scaling as the non-relativistic counterpart, where only the one- and two-body density cumulants are required to obtain the vertical transition energy. The accuracy of BP1-SA-DSRG-PT2c is assessed on a few atoms and small molecules, including main-group diatomic molecules, transition-metal atoms, and actinide dioxide cations. Numerical results suggest that BP1-SA-DSRG-PT2c performs comparably to other internally contracted multireference perturbation theories with SOC treated using the state interaction scheme. Full article

Entropic Dynamics (ED) provides a framework that allows the reconstruction of the formalism of quantum mechanics by insisting on ontological and epistemic clarity and adopting entropic methods and information geometry. Our present goal is to extend the ED framework to account for spin. The result is a realist $\psi$-epistemic model in which the ontology consists of a particle described by a definite position plus a discrete variable that describes Pauli’s peculiar two-valuedness. The resulting dynamics of probabilities is, as might be expected, described by the Pauli equation. What may be unexpected is that the generators of transformations—Hamiltonians and angular momenta, including spin, are all granted clear epistemic status. To the old question, ‘what is spinning?’ ED provides a crisp answer: nothing is spinning. Full article

While either a spin or point-group adaptation is straightforward when considered independently, the standard technique for factoring isotropic spin Hamiltonians by the total spin S and the irreducible representation $\mathsf{\Gamma }$ of the point group is limited by the complexity of the transformations between different coupling schemes that are related in terms of their site permutations. To overcome these challenges, we apply projection operators directly to uncoupled basis states, enabling the simultaneous treatment of spin and point-group symmetry without the need for recoupling transformations. This provides a simple and efficient approach for the exact diagonalization of isotropic spin models, which we illustrate, with applications in Heisenberg spin rings and polyhedra, including systems that are computationally inaccessible with conventional coupling techniques. Full article

We introduce the concept of ergodicity and explore its deviation caused by quantum scars in an isolated quantum system, employing a pedagogical approach based on a toy model. Quantum scars, originally identified as traces of classically unstable orbits in certain wavefunctions of chaotic systems, have recently regained interest for their role in non-ergodic dynamics, as they retain memory of their initial states. We elucidate these features of quantum scars within the same framework of this toy model. The integrable part of the model consists of two large spins, with a classical counterpart, which we combine with a random matrix to induce ergodic behavior. Scarred states can be selectively generated from the integrable spin Hamiltonian by protecting them from the ergodic states using a projector method. Deformed projectors mimic the ‘quantum leakage’ of scarred states, enabling tunable mixing with ergodic states and thereby controlling the degree of scarring. In this simple model, we investigate various properties of quantum scarring and shed light on different aspects of many-body quantum scars observed in more complex quantum systems. Notably, the underlying classicality can be revealed through the entanglement spectrum and the dynamics of ‘out-of-time-ordered correlators’. Full article

The spin Hall effect for the model Hamiltonian of graphene with Rashba spin–orbit coupling is analyzed by means of a recently derived quantum kinetic theory of the linear response for multi-band electron systems. The latter expresses the interband part of the density matrix in terms of the intraband occupation numbers, which can be obtained as solutions of a Boltzmann transport equation. The analysis, which, in the case of the model here considered, can be carried out in a completely analytical way, thus provides an effective pedagogical illustration of the general theory. While our results agree with those previously obtained with alternative approaches for the same model, our comparatively simpler and more physically transparent derivation illustrates the advantages of our formalism when dealing with non trivial multi-band Hamiltonians. Full article

Understanding the flow, loss, and recovery of the information between a system and its environment is essential for advancing quantum technologies. The central spin system serves as a useful model for a single qubit, offering valuable insights into how quantum systems can be manipulated and protected from decoherence. This work uses the stimulated echo experiment to track the information flow between the central spin and its environment, providing a direct measure of the sensitivity of system/environment correlations to environmental dynamics. The extent of mixing and the growth of correlations are quantified through autocorrelation functions of the noise and environmental dynamics, which also enable the estimation of nested commutators between the system/environment and environmental Hamiltonians. Complementary decoupling experiments offer a straightforward measure of the strength of the system Hamiltonians. The approach is experimentally demonstrated on a spin system. Full article

In this study, we report the syntheses, crystal structures and magnetic properties of ternary copper(II) coordination compounds with l-homoserine (l-Hhser) and 1,10-phenanthroline (phen). Six new coordination compounds were obtained: [Cu(l-hser)(H₂O)(phen)]₂SO₄·5H₂O (1·5H₂O), [Cu(μ-l-hser)(H₂O)(phen)][Cu(l-hser)(H₂O)(phen)]₃(SO₄)₂∙12H₂O (2·12H₂O), {[Cu(μ-l-hser)(H₂O)(phen)][Cu(μ-l-hser)(phen)]SO₄·6H₂O}_n (3·6H₂O), {[Cu(μ-l-hser)(H₂O)(phen)]₂SO₄·3H₂O}_n (4·3H₂O), [Cu(l-hser)(H₂O)(phen)][Cu(l-hser)(CH₃OH)(phen)]SO₄·4H₂O (5·4H₂O) and {[Cu(l-hser)(CH₃OH)(phen)][Cu(μ-l-hser)(phen)]SO₄·5CH₃OH}_n (6·5CH₃OH). It was shown that slight differences in water content in the synthetic mixtures highly influence the final product, so in some cases, two or three different products were obtained. The compounds were characterized by single-crystal X-ray diffraction and ESR spectroscopy. Crystal packings are based on intensive networks of hydrogen bonds and π interactions. Most water solvent molecules in these microporous compounds are found in discrete pockets (1∙5H₂O, 2∙12H₂O, 3∙6H₂O, 4∙3H₂O). In 5∙4H₂O, water molecules are packed in pockets and 1D channels and in 6∙5CH₃OH methanol solvent molecules form 1D channels. ESR spectroscopy measured from room down to liquid nitrogen temperature was used for local magnetic characterization of copper centers. The spin Hamiltonian parameters obtained from the spectral simulation revealed copper coordination geometry that is in agreement with the structural results. Furthermore, ESR spectra revealed no significant exchange coupling between copper ions. 3·6H₂O showed pronounced antiproliferative activity toward human colon cancer cell lines (HCT116), human breast cancer cell line (MCF-7) and human lung cancer cell lines (H460). Full article

We introduce a new approach for describing nonstationary quantum systems with a discrete energy spectrum. The essence of this approach is that we describe the evolution of a quantum system in a time-dependent basis. In a sense, this approach is similar to the description of the system in the interaction representation. However, the time dependence of the basic states of the representation is determined not by the evolution operator with a time-independent Hamiltonian but by the eigenstates of the time-dependent Hamiltonian defined at the current time. The time dependence of the basic states of the representation leads to the appearance of an additional term in the Schrödinger equation, which in the case of slowly changing parameters of the Hamiltonian can be considered as a small perturbation. The adiabatic representation is suitable in cases where it is impossible to apply the standard interaction representation. The application of the adiabatic representation is illustrated by the example of two spins connected by a magnetic dipole–dipole interaction in a slowly varying external magnetic field. Full article

A consistent theory of quantum entanglement requires that constituent single-particle states belong to the same Hilbert space, the coherent eigenstates of a complete set of operators in a given representation, defined with respect to a shared continuous parameterization. Formulating such eigenstates for a single relativistic particle with spin, and applying them to the description of many-body states, presents well-known challenges. In this paper, we review the covariant theory of relativistic spin and entanglement in a framework first proposed by Stueckelberg and developed by Horwitz, Piron, et al. This approach modifies Wigner’s method by introducing an arbitrary timelike unit vector $n^{\mu }$ and then inducing a representation of $SL(2,C)$, based on $p^{\mu }$ rather than on the spacetime momentum. Generalizing this approach, we construct relativistic spin states on an extended phase space $\{(x^{\mu },p^{\mu }),({\zeta }^{\mu },{\pi }^{\mu })\}$, inducing a representation on the momentum ${\pi }^{\mu }$, thus providing a novel dynamical interpretation of the timelike unit vector $n^{\mu }={\pi }^{\mu }/M$. Studying the unitary representations of the Poincaré group on the extended phase space allows us to define basis quantities for quantum states and develop the gauge invariant electromagnetic Hamiltonian in classical and quantum mechanics. We write plane wave solutions for free particles and construct stable singlet states, and relate these to experiments involving temporal interference, analogous to the spatial interference known from double slit experiments. Full article

We propose spin models that can display an arbitrary number of phase transitions. The models are based on the standard $XY$ model, which is generalized by including higher-order nematic terms with exponentially increasing order and linearly increasing interaction strength. By employing Monte Carlo simulation we demonstrate that under certain conditions the number of phase transitions in such models is equal to the number of terms in the generalized Hamiltonian and, thus, it can be predetermined by construction. The proposed models produce the desirable number of phase transitions by solely varying the temperature. With decreasing temperature the system passes through a sequence of different phases with gradually decreasing symmetries. The corresponding phase transitions start with a presumably BKT transition that breaks the U(1) symmetry of the paramagnetic phase, and they proceed through a sequence of discrete ${\mathbb{Z}}_2$ symmetry-breaking transitions between different nematic phases down to the lowest-temperature ferromagnetic phase. Full article