Search Results (159)

The recently proposed conformable deformation of quantum mechanics by a fractional parameter $\alpha \in (0,1]$ has been used to construct a conformable quantum harmonic oscillator, which coincides with the standard quantum oscillator at $\alpha =1$. We argue that there is a conformable generalization of the uncertainty principle and use it to define the conformable coherent states of the conformable quantum oscillator along the general line of quantum mechanics. We investigate the fundamental physical and mathematical properties of these states in the $x^{\alpha }$-representation. In particular, we determine these states from the minimum uncertainty, compute their energy, find their conformable time-dependent form, determine the conformable translation operator, and show that conformable coherent states are eigenstates of the conformable annihilation operator. These states reproduce in the $\alpha =1$ limit of the correspondence principle the coherent states of the standard quantum harmonic oscillator. Full article

We present an analytical framework for describing light propagation in infinite waveguide arrays, incorporating a generalized long-range coupling to achieve a more realistic model. We demonstrate that the resulting solution can be expressed in terms of generalized Bessel-like functions. Additionally, by applying the concept of eigenstates, we borrow from quantum mechanics a basis given in terms of phase states that allows the analysis of the transition from the discrete to the continuum limit, obtaining a relationship between the field amplitudes and the Fourier series coefficients of a given function. We apply our findings to different coupling functions, providing new insights into the propagation dynamics of these systems. Full article

One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via explicit time evolution for the generic model system of an interacting, trapped Bose gas with discrete single-particle levels, how the measurement of one or more observables subdivides the system into observed and non-observed Hilbert subspaces and the tracing over the non-measured quantum numbers defines an effective, thermodynamic bath, induces the entanglement of the observed Hilbert subspace with the bath, and leads to a bi-exponential approach of the entanglement entropy and of the measured observables to thermal equilibrium behavior as a function of time. We find this to be more generally fulfilled than in the scenario of the eigenstate thermalization hypothesis (ETH), namely for both local particle occupation numbers and non-local density correlation functions, and independent of the specific initial quantum state of the time evolution. Full article

Semiconductors underpin modern technology, enabling applications from power electronics and photovoltaics to communications and medical diagnostics. However, the industry faces pressing challenges, including shortages of critical raw materials and the unsustainable nature of conventional fabrication processes. Recent developments in quantum computing and topological quantum materials offer a transformative path forward. In particular, materials exhibiting non-Hermitian physics and topological protection, such as topological insulators and superconductors, enable robust, energy-efficient electronic states. These states are resilient to disorder and local perturbations, positioning them as ideal candidates for next-generation quantum devices. Non-Hermitian systems, which break traditional Hermitian constraints, have revealed phenomena like the skin effect, wherein eigenstates accumulate at boundaries, violating bulk-boundary correspondence. This effect has recently been observed in semiconductor-based quantum Hall devices, marking a significant milestone in condensed matter physics. By integrating these non-Hermitian topological principles into semiconductor technology, researchers can unlock new functionalities for fault-tolerant quantum computing, low-power electronics, and ultra-sensitive sensing platforms. This convergence of topology, quantum physics, and semiconductor engineering may redefine the future of electronic and photonic devices. Full article

Revealing singular quantum phenomena in various non-Hermitian systems is a hot topic in condensed matter physics research, with the bulk-boundary correspondence being one of the core issues in non-Hermitian topological states. In addition, the spin-orbit coupling (SOC) applied to electrons moving in the electric field in the material can bring unique topological properties to the energy band of the material. We investigated the topological phase transition of a non-Hermitian Su–Schrieffer–Heeger (SSH) model with SOC in the generalized Brillouin zone (GBZ). We demonstrate that SOC can alter the position and number of phase transition points. Due to the non-Hermitian skin effect, the bulk-boundary correspondence is broken, and the local positions of zero mode and bulk eigenstates will also change. By unitary transformation, two subspaces were obtained, and the exact solution of topological phase transition was obtained in the GBZ. The exact solution of non-Hermitian systems with the Dresselhaus and Rashba types of SOC is consistent with the numerical solutions. This result can be applied to more complex non-Hermitian models, providing a strong reference for experimental researchers in topological materials. Full article

We present a generalized Floquet Hamiltonian method for dispersive photonic time crystals (PTCs), a class of time-varying media with time-periodic plasma frequencies and damping rates. Using the time-independent Floquet Hamiltonian method, we successfully obtained the quasienergy band dispersions of dispersive PTCs, which show excellent agreement with the temporal transfer matrix method (TTMM) results when applied to temporal multilayers. Furthermore, our approach overcomes the limitations of TTMM by handling arbitrary time interfaces and providing access to both right and left eigenstates, enabling deeper insights into the properties of PTCs. Ultimately, our method significantly advances the analytical and numerical investigations into dispersive time-varying media. Full article

A notable feature of systems with non-Hermitian skin effects is the sensitivity to boundary conditions. In this work, we introduce one type of boundary condition provided by a coupling impurity. We consider a system where a two-level system as an impurity couples to a nonreciprocal Su–Schrieffer–Heeger chain under periodic boundary conditions at two points with asymmetric couplings. We first study the spectrum of the system and find that asymmetric couplings lead to topological phase transitions. Meanwhile, a striking feature is that the coupling impurity can act as an effective boundary, and asymmetric couplings can also induce a flexibly adjusted zero mode. It is localized at one of the two effective boundaries or both of them by tuning coupling strengths. Moreover, we uncover three types of localization behaviors of eigenstates for this non-Hermitian impurity system with on-site disorder. These results corroborate the potential for control of a class of non-Hermitian systems with coupling impurities. Full article

The reduced density matrix that characterises the state of an open quantum system is a projection from the full density matrix of the quantum system and its environment, and there are many full density matrices consistent with a given reduced version. Without a specification of relevant details of the environment, the time evolution of a reduced density matrix is therefore typically unpredictable, even if the dynamics of the full density matrix are deterministic. With this in mind, we investigate a two-level open quantum system using a framework of quantum state diffusion. We consider the pseudorandom evolution of its reduced density matrix when subjected to an environment-driven process that performs a continuous quantum measurement of a system observable, invoking dynamics that asymptotically send the system to one of the relevant eigenstates. The unpredictability is characterised by a stochastic entropy production, the average of which corresponds to an increase in the subjective uncertainty of the quantum state adopted by the system and environment, given the underspecified dynamics. This differs from a change in von Neumann entropy, and can continue indefinitely as the system is guided towards an eigenstate. As one would expect, the simultaneous measurement of two non-commuting observables within the same framework does not send the system to an eigenstate. Instead, the probability density function describing the reduced density matrix of the system becomes stationary over a continuum of pure states, a situation characterised by zero further stochastic entropy production. Transitions between such stationary states, brought about by changes in the relative strengths of the two measurement processes, give rise to finite positive mean stochastic entropy production. The framework investigated can offer useful perspectives on both the dynamics and irreversible thermodynamics of measurement in quantum systems. Full article

Quantum information scrambling refers to the spread of the initially stored information over many degrees of freedom of a quantum many-body system. Information scrambling is intimately linked to the thermalization of isolated quantum many-body systems, and has been typically studied in a sudden quench scenario. Here, we extend the notion of quantum information scrambling to critical quantum many-body systems undergoing an adiabatic evolution. In particular, we analyze how the symmetry-breaking information of an initial state is scrambled in adiabatically driven integrable systems, such as the Lipkin–Meshkov–Glick and quantum Rabi models. Following a time-dependent protocol that drives the system from symmetry-breaking to a normal phase, we show how the initial information is scrambled, even for perfect adiabatic evolutions, as indicated by the expectation value of a suitable observable. We detail the underlying mechanism for quantum information scrambling, its relation to ground- and excited-state quantum phase transitions, and quantify the degree of scrambling in terms of the number of eigenstates that participate in the encoding of the initial symmetry-breaking information. While the energy of the final state remains unaltered in an adiabatic protocol, the relative phases among eigenstates are scrambled, and so is the symmetry-breaking information. We show that a potential information retrieval, following a time-reversed protocol, is hindered by small perturbations, as indicated by a vanishingly small Loschmidt echo and out-of-time-ordered correlators. The reported phenomenon is amenable for its experimental verification, and may help in the understanding of information scrambling in critical quantum many-body systems. 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 present a Gordon decomposition of the magnetizability of a Dirac one-electron atom in an arbitrary discrete energy eigenstate, with a pointlike, spinless, and motionless nucleus of charge $Ze$. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, static, and uniform. Using the Sturmian expansion of the generalized Dirac–Coulomb Green function proposed by Szmytkowski in 1997, we derive a closed-form expressions for the diamagnetic (${\chi }_d$) and paramagnetic (${\chi }_p$) contributions to $\chi$. Our calculations are purely analytical; the received formula for ${\chi }_p$ contains the generalized hypergeometric functions ₃F₂ of the unit argument, while ${\chi }_d$ is of an elementary form. For the atomic ground state, both results reduce to the formulas obtained earlier by other author. This work is a prequel to our recent article, where the numerical values of ${\chi }_d$ and ${\chi }_p$ for some excited states of selected hydrogenlike ions with $1⩽Z⩽137$ were obtained with the use of the general formulas derived here. Full article

For a long time, it was presumed that continuum bands could be readily encompassed by open-boundary spectra, irrespective of the system’s modest dimensions. However, our findings reveal a nuanced picture: under open-boundary conditions, the proliferation of complex eigenvalues progresses in a sluggish, oscillating manner as the system expands. Consequently, even in larger systems, the overlap between continuum bands and open-boundary eigenvalues becomes elusive, with the surprising twist that the count of these complex eigenvalues may actually diminish with increasing system size. This counterintuitive trend underscores that the pursuit of an ideal, infinite-sized system scenario does not necessarily align with enlarging the system size. Notably, despite the inherent non-Hermiticity of our system, the eigenstates distribute themselves in a manner reminiscent of Bloch waves. These discoveries hold potential significance for both theoretical explorations and experimental realizations of non-Hermitian systems. Full article

Spin Hamiltonians, like the Heisenberg model, are used to describe the magnetic properties of exchange-coupled molecules and solids. For finite clusters, physical quantities, such as heat capacities, magnetic susceptibilities or neutron-scattering spectra, can be calculated based on energies and eigenstates obtained by exact diagonalization (ED). Utilizing spin-rotational symmetry SU(2) to factor the Hamiltonian with respect to total spin S facilitates ED, but the conventional approach to spin-adapting the basis is more intricate than selecting states with a given magnetic quantum number M (the spin z-component), as it relies on irreducible tensor-operator techniques and spin-coupling coefficients. Here, we present a simpler technique based on applying a spin projector to uncoupled basis states. As an alternative to Löwdin’s projection operator, we consider a group-theoretical formulation of the projector, which can be evaluated either exactly or approximately using an integration grid. An important aspect is the choice of uncoupled basis states. We present an extension of Löwdin’s theorem for $s=\frac{1}{2}$ to arbitrary local spin quantum numbers s, which allows for the direct selection of configurations that span a complete, linearly independent basis in an S sector upon the spin projection. We illustrate the procedure with a few examples. Full article

In this work, we study the time-dependent behavior of quantum correlations of a system of an inverted oscillator governed by out-of-equilibrium dynamics using the well-known Schwinger–Keldysh formalism in the presence of quantum mechanical quench. Considering a generalized structure of a time-dependent Hamiltonian for an inverted oscillator system, we use the invariant operator method to obtain its eigenstate and continuous energy eigenvalues. Using the expression for the eigenstate, we further derive the most general expression for the generating function as well as the out-of-time-ordered correlators (OTOCs) for the given system using this formalism. Further, considering the time-dependent coupling and frequency of the quantum inverted oscillator characterized by quench parameters, we comment on the dynamical behavior, specifically the early, intermediate and late time-dependent features of the OTOC for the quenched quantum inverted oscillator. Next, we study a specific case, where the system of an inverted oscillator exhibits chaotic behavior by computing the quantum Lyapunov exponent from the time-dependent behavior of OTOCs in the presence of the given quench profile. Full article