Search Results (18)

The turning point that sparked the initiation of quantum theory was the Planck–Einstein postulate that the energy of a monochromatic radiation field is quantized in terms of photons, and this was followed by the development of the principles of quantum mechanics. Although some conceptual issues remain to be resolved, quantum mechanics is regarded as a well-established discipline which may lead to the unraveling of the nature of matter in general. Today, the influence of quantum mechanics is evident in its applications, with remarkable technological advances involving diverse aspects of the physical world. What appears to need particular attention, however, (after a hundred years have elapsed since the birth of quantum mechanics) is the impact that the concept of the ‘quantum’ has had beyond traditional quantum mechanics. The paper describes how the ‘quantum’ concept has influenced and continues to influence developments in physical systems, which are essentially classical, in that they are basically governed, entirely, or in part, by non-quantum laws, but in which, the physics is distinguished by its own special quantum—the photon analogue. The paper illustrates this by considering, as prototype examples, bulk plasmons and phonons. The study outlines the systematic quantization of plasmons and phonons, both of the polariton (transverse) forms and their longitudinal forms, and discusseshow these interact with quantum systems such as electrons, atoms, and condensed matter. It is demonstarted using one case, namely, involving longitudinal plasmons, how utilizing quantum concepts and techniques facilitate their interaction with matter, as in electron energy loss spectroscopy. Full article

The quantum dissipative time evolution of a fluxonium under a pulsed field (kicks) is studied numerically and analytically. In the classical limit, the system dynamics is converged to a strange chaotic attractor. The quantum properties of this system are studied using the density matrix within the framework of the Lindblad equation. In the case of dissipative quantum evolution, the steady-state density matrix is converged to a quantum strange attractor that is similar to the classical one. It is shown that depending on the dissipation strength, there is a regime when the eigenstates of the density matrix are localized at a strong or moderate dissipation. At weak dissipation, the eigenstates are argued to be delocalized, which is linked to the Ehrenfest explosion of the quantum wave packet. This phenomenon is related to the Lyapunov exponent and Ehrenfest time for the quantum strange attractor. Possible experimental realizations of this quantum strange attractor with fluxonium are discussed. Full article

This review explores the foundations of non-relativistic quantum electrodynamics (QED) and its application to atoms and molecules. It follows the traditional route of placing classical electrodynamics in an Hamiltonian framework, followed by Dirac’s canonical quantisation algorithm. The properties of the resulting quantum Hamiltonian are reviewed from a non-perturbative perspective. It discusses the gauge invariance of the S-matrix, the Coulomb interaction, and the challenges posed by infinities in classical and quantum electrodynamics. The paper examines the mathematical frameworks used to address these issues, including the use of distributions and the Colombeau algebra. The review also highlights the limitations of the Coulomb Hamiltonian in explaining molecular structure and chemistry, emphasizing the need for additional theoretical modifications to bridge quantum mechanics and chemical phenomena. Full article

We address the spatially nonlocal dielectric functions of graphene at any frequency derived starting from the first principles of thermal quantum field theory using the formalism of the polarization tensor. After a brief review of this formalism, the longitudinal and transverse dielectric functions are considered at any relationship between the frequency and the wave vector. The analytic properties of their real and imaginary parts are investigated at low and high frequencies. Emphasis is given to the double pole at zero frequency, which arises in the transverse dielectric function. The role of this unusual property in solving the problem of disagreement between experiment and theory in the Casimir effect is discussed. We believe that a more complete dielectric response of ordinary metals should also be spatially nonlocal and its transverse part may possess the double pole in the region of evanescent waves. Full article

We present a brief review of a nontraditional but significant application for a high-temperature charged plasma. The unorthodox proposition was made by Barry Ninham concerning a contribution from Casimir forces across high-temperature electron–positron plasma in nuclear interactions. The key message in this review is that high temperatures (about ${10}^{11}$ K) are found to be essential. Certainly, classical, semi-classical, and quantum considerations for the background media impact both the Casimir effect and the physics of stars and the Universe. Full article

We analyze shortcuts to adiabaticity (STA) and their completions for the quantum harmonic oscillator (QHO) with time-dependent frequency, as well as for quantum field theory (QFT) in non-stationary backgrounds. We exploit the analogy with one-dimensional quantum mechanics, and the known correspondence between Bogoliubov coefficients in the QHO and transmission/reflection amplitudes in scattering theory. Within this framework, STA protocols for the QHO are equivalent to transmission resonances, while STA in QFT with homogeneous backgrounds correspond to reflectionless potentials. Moreover, using the connection between particle creation and squeezed states, we show how STA completions can be understood in terms of the anti-squeezing operator. Full article

We present two complementary approaches to the Gorini–Kossakowski–Sudarshan–Lindblad equation for an open qubit. First, based on linearity, yields solutions illustrated by mixed-state trajectories in the Bloch ball, including non-random asymptotic fixed points and exceptional points. Second, exploiting the SU$\left(2\right)$ symmetry, leads to a nonlinear dynamical system that separates angular dynamics from radial dissipation. This symmetry-based perspective presents a promising route toward generalization to open qudits. Full article

The quantizer–dequantizer method is employed. Using the construction of probability distributions describing density operators of a quantum system states, the connection between the Feynman path integral and the time evolution of the density operator (Landau density matrix) as well as the wave function of the stateconsidered. For single–mode systems with continuous variables, a tomographic propagator is introduced in the probability representation of quantum mechanics. An explicit expression for the probability in terms of the Green function of the Schrödinger equation is obtained. Equations for the Green functions defined by arbitrary integrals of motion are derived. Examples of probability distributions describing the evolution of state of a free particle, as well as states of systems with integrals of motion that depend on time (oscillator type) are discussed. Full article

Molecular quantum electrodynamics is a powerful and effective tool for the representation and elucidation of optical interactions with matter. Its history spans nearly a century of significant advances in its detailed theory and applications, and in its wider appreciation. To fully appreciate the development of the subject into its modern form invites a perspective on progressive technical progress in the theory, noting a growth in applications that closely mirrors advances in optical experimentation. The challenges and deficiencies of alternative approaches to theory are also taken into consideration. Full article

This paper for the first time derives some properties of the hydrogen atom inside a box with an impenetrable wall. Scaling of the Hamiltonian operator proves to be practical for the derivation of some general properties of the eigenvalues. The radial part of the Schrödinger equation is conditionally solvable and the exact polynomial solutions provide helpful information. There are accidental degeneracies that take place at particular values of the box radius, some of which can be determined from the conditionally-solvable condition. Some of the roots stemming from the conditionally-solvable condition appear to converge towards the critical values of the model parameter. This analysis is facilitated by the Rayleigh–Ritz method that provides accurate eigenvalues. Full article

The steady-state quantum dynamics of a compound sample consisting of a semiconductor double-quantum-dot (DQD) system, non-linearly coupled with a leaking superconducting transmission line resonator, is theoretically investigated. Particularly, the transition frequency of the DQD is taken to be equal to the doubled resonator frequency, whereas the inter-dot Coulomb interaction is considered weak. As a consequence, the steady-state quantum dynamics of this complex non-linear system exhibit sudden changes in its features, occurring at a critical DQD-cavity coupling strength, suggesting perspectives for designing on-chip microwave quantum switches. Furthermore, we show that, above the threshold, the electrical current through the double-quantum dot follows the mean photon number into the microwave mode inside the resonator. This might not be the case any more below that critical coupling strength. Lastly, the photon quantum correlations vary from super-Poissonian to Poissonian photon statistics, i.e., towards single-qubit lasing phenomena at microwave frequencies. Full article

In special relativity, particle trajectories, whether mass-bearing or not, can be traced on the Minkowski spacetime manifold in (3+1)D. Meantime, in quantum mechanics, trajectories in the phase space are not strictly outlined because coordinate and linear momentum cannot be measured simultaneously with arbitrary precision since they do not commute within the Hilbert space formalism. However, from the density matrix representing a quantum system, the extracted information still produces an imperative description of its properties and, furthermore, by appropriately reordering the matrix entries, additional information can be obtained from the same content. Adhering to this line of work, the paper investigates the definition and the meaning of velocity and speed in a typical quantum phenomenon, the disentanglement for a bipartite system when dynamical evolution is displayed in a (3+1)D pseudo-spacetime whose coordinates are constructed from combinations of entries to the density matrix. The formalism is based on the definition of a Minkowski manifold with compact support, where trajectories are defined following the same reasoning and formalism present in the Minkowski manifold of special relativity. The space-like and time-like regions acquire different significations referred to entangled-like and separable-like, respectively. The definition and the sense of speed and velocities of disentanglement follow naturally from the formalism. Depending on the dynamics of the physical state of the system, trajectories may meander between regions of entanglement and separability in the space of new coordinates defined on the Minkowski manifold. Full article

Measurement uncertainty limits how precisely information can be extracted from quantum systems due to inherent quantum indeterminacy. On the other hand, dense coding capacity quantifies the amount of classical information that can be sent using shared entanglement, thereby enhancing communication efficiency beyond classical limits. In this paper, we investigate these two concepts for a spin-star network under an external magnetic field under a thermal regime, considering both homogeneous and inhomogeneous models. We reveal that under certain conditions, dense coding capacity not only becomes valid but is also optimized, implying that measurement uncertainty is significantly suppressed. Furthermore, we analyze the local quantum uncertainty of the thermal state under the influence of decoherence channels to assess the effectiveness of the approach studied. Full article

We compare the semiclassical and quantum predictions for the unitary dynamics of a two-level atom interacting with a single-mode electromagnetic field under parametric modulation of the atomic parameters in the regime of multiphoton atom–field resonances. We derive approximate analytic solutions for the semiclassical Rabi model when the atomic transition frequency and the atom–field coupling strength undergo harmonic external modulations. These solutions are compared to the predictions of the quantum Rabi model, which we solve numerically for an initial coherent state with a large average photon number (on the order of ${10}^4$), in the regime of three-photon resonance. We show that, for short enough times and sufficiently intense coherent states, the semiclassical dynamics agrees quite well with the quantum dynamics, although it inevitably fails at longer times due to the absence of collapse–revival behavior. Furthermore, we describe how the field state evolves throughout the interaction, presenting numerical results for the average photon number, entropies (related to atom–field entanglement), and other quantities characterizing the photon number statistics of the electromagnetic field. Full article

The paper presents a survey of some dynamical transitions in nonequilibrium trapped Bose-condensed systems subject to the action of alternating fields. Nonequilibrium states of trapped systems can be implemented in two ways: resonant and nonresonant. Under resonant excitation, several coherent modes are generated by external alternating fields with the frequencies been tuned to resonance with some transition frequencies of the trapped system. A Bose system of trapped atoms with Bose–Einstein condensate can display two types of the Josephson effect, the standard one, when the system is separated into two or more parts in different locations, or the internal Josephson effect, when there are no any separation barriers but the system becomes nonuniform due to the coexistence of several coherent modes interacting one with another. The mathematics in both these cases is similar. We focus on the internal Josephson effect. Systems with nonlinear coherent modes demonstrate rich dynamics, including Rabi oscillations, the Josephson effect, and chaotic motion. Under the Josephson effect, there exist dynamic transitions that are similar to phase transitions in equilibrium systems. The bosonic Josephson effect is shown to be implementable not only for quite weakly interacting systems, but also in superfluids with not necessarily as weak interactions. Sufficiently strong nonresonant excitation can generate several types of nonequilibrium states comprising vortex germs, vortex rings, vortex lines, vortex turbulence, droplet turbulence, and wave turbulence. Nonequilibrium states are shown to be characterized and distinguished by effective temperature, effective Fresnel number, and dynamic scaling laws. Full article