Search Results (89)

We follow the assumption that relativistic causality is a key element in the structure of quantum mechanics and integrate the speed of light, c, into quantum mechanics through the postulate that the (reduced) Planck constant is a function of c with a leading order of the form $\hslash \left(c\right)\sim \mathsf{\Lambda }/c^p$ for a constant $\mathsf{\Lambda }>0,$ and $p>1.$ We show how the limit $c\to \infty$ implies classicality in quantum mechanics and explain why p has to be larger than $1$. As the limit $c\to \infty$ breaks down both relativity theory and quantum mechanics, as followed by the proposed model, it can then be understood through similar conceptual physical laws. We further show how the position-dependent speed of light gives rise to an effective curved space in quantum systems and show that a stronger gravitational field implies higher quantum uncertainties, followed by the varied $c.$ We then discuss possible ways to find experimental evidence of the proposed model using set-ups to test the varying speed of light models and examine analogies of the model based on electrons in semiconductor heterostructures. Full article

The simulation analogy presented in this work enhances the accessibility of abstract quantum theories, specifically the stochastic hydrodynamic model (SQHM), by relating them to our daily experiences. The SQHM incorporates the influence of fluctuating gravitational background, a form of dark energy, into quantum equations. This model successfully addresses key aspects of objective-collapse theories, including resolving the ‘tails’ problem through the definition of quantum potential length of interaction in addition to the De Broglie length, beyond which coherent Schrödinger quantum behavior and wavefunction tails cannot be maintained. The SQHM emphasizes that an external environment is unnecessary, asserting that the quantum stochastic behavior leading to wavefunction collapse can be an inherent property of physics in a spacetime with fluctuating metrics. Embedded in relativistic quantum mechanics, the theory establishes a coherent link between the uncertainty principle and the constancy of light speed, aligning seamlessly with finite information transmission speed. Within quantum mechanics submitted to fluctuations, the SQHM derives the indeterminacy relation between energy and time, offering insights into measurement processes impossible within a finite time interval in a truly quantum global system. Experimental validation is found in confirming the Lindemann constant for solid lattice melting points and the ⁴He transition from fluid to superfluid states. The SQHM’s self-consistency lies in its ability to describe the dynamics of wavefunction decay (collapse) and the measure process. Additionally, the theory resolves the pre-existing reality problem by showing that large-scale systems naturally decay into decoherent states stable in time. Continuing, the paper demonstrates that the physical dynamics of SQHM can be analogized to a computer simulation employing optimization procedures for realization. This perspective elucidates the concept of time in contemporary reality and enriches our comprehension of free will. The overall framework introduces an irreversible process impacting the manifestation of macroscopic reality at the present time, asserting that the multiverse exists solely in future states, with the past comprising the formed universe after the current moment. Locally uncorrelated projective decays of wavefunction, at the present time, function as a reduction of the multiverse to a single universe. Macroscopic reality, characterized by a foam-like consistency where microscopic domains with quantum properties coexist, offers insights into how our consciousness perceives dynamic reality. It also sheds light on the spontaneous emergence of gravity in discrete quantum spacetime evolution, and the achievement of the classical general relativity limit in quantum loop gravity and causal dynamical triangulation. The simulation analogy highlights a strategy focused on minimizing information processing, facilitating the universal simulation in solving its predetermined problem. From within, reality becomes the manifestation of specific physical laws emerging from the inherent structure of the simulation devised to address its particular issue. In this context, the reality simulation appears to employ an optimization strategy, minimizing information loss and data management in line with the simulation’s intended purpose. Full article

The combination of ion exchange membranes with carbon quantum dots (CQDs) is a promising field that could lead to significant advances in water treatment. Composite membranes formed by sulfonated poly(ether ether ketone) (SPEEK) with embedded CQDs were used for the detection and removal of heavy metal ions, such as lead and cadmium, from water. SPEEK is responsible for the capture of heavy metals based on the cation exchange mechanism, while CQDs detect their contamination by exhibiting changes in fluorescence. Water-insoluble “red” carbon quantum dots (rCQDs) were synthesized from p-phenylenediamine so that their photoluminescence was shifted from that of the polymer matrix. CQDs and the composites were characterized by several techniques: FTIR, Raman, UV/VIS, photoluminescence, XPS spectroscopies, and AFM microscopy. The heavy metal ion concentration was analyzed by inductively coupled plasma–optical emission spectroscopy (ICP-OES). The concentration ranges were 10.8–0.1 mM for Pb²⁺ and 10.0–0.27 mM for Cd²⁺. SPEEK/rCQDs showed a more pronounced turn-off effect for lead. The composite achieved 100% removal efficiency for lead and cadmium when the concentration was below a half of the ion exchange capacity of SPEEK. The regeneration of membranes in 1 M NaCl was also studied. A second order law was effective to describe the kinetics of the process. Full article

Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an extremely restricted subspace of the Hilbert space that seems “conspiratorial”, in the sense that (1) it seems to depend on future events that involve records (including measurement settings) and on the dynamical law (normally thought to be independent of the initial conditions), and (2) it violates Statistical Independence, even when it is valid in the context of Bell’s theorem. To solve the puzzle, I build a model in which, by changing the dynamical law, the same initial conditions can lead to different histories in which the validity of records is relative to the new dynamical law. This relative validity of the records may restore causality, but the initial conditions still must depend, at least partially, on the dynamical law. While violations of Statistical Independence are often seen as non-scientific, they turn out to be needed to ensure the validity of records and our own memories and, by this, of science itself. A Past Hypothesis is needed to ensure the existence of records and turns out to require violations of Statistical Independence. It is not excluded that its explanation, still unknown, ensures such violations in the way needed by local interpretations of quantum mechanics. I suggest that an as-yet unknown law or superselection rule may restrict the full tensor-product Hilbert space to the very special subspace required by the validity of records and the Past Hypothesis. Full article

Graphene–silicon Schottky diodes are intriguing devices that straddle the border between classical models and two-dimensional ones. Many papers have been published in recent years studying their operation based on the classical model developed for metal–silicon Schottky diodes. However, the results obtained for diode parameters vary widely in some cases showing very large deviations with respect to the expected range. This indicates that our understanding of their operation remains incomplete. When modeling these devices, certain aspects strictly connected with the quantum mechanical features of both graphene and the interface with silicon play a crucial role and must be considered. In particular, the dependence of the graphene Fermi level on carrier density, the relation of the latter with the density of surface states in silicon and the coupling between in-plane and out-of-plane dynamics in graphene are key aspects for the interpretation of their behavior. Within the thermionic regime, we estimate the zero-bias Schottky barrier height and the density of silicon surface states in graphene/type-p silicon diodes by adapting a kown model and extracting ideality index values close to unity. The ohmic regime, beyond the flat band potential, is modeled with an empirical law, and the current density appears to be roughly proportional to the electric field at the silicon interface; moreover, the graphene-to-silicon electron tunneling efficiency drops significantly in the transition from the thermionic to ohmic regime. We attribute these facts to (donor) silicon surface states, which tend to be empty in the ohmic regime. Full article

The Second Quantum Revolution refers to a contemporary wave of advancements and breakthroughs in the field of quantum physics that extends beyond the early developments of Quantum Mechanics that occurred in the 20th century. One crucial aspect of this revolution is the deeper exploration and practical application of quantum entanglement. Entanglement serves as a cornerstone in the ongoing revolution, contributing to quantum computing, communication, fundamental physics experiments, and advanced sensing technologies. Here, we present and discuss some of the recent applications of entanglement, exploring its philosophical implications and non-locality beyond Bell’s theorem, thereby critically examining the foundations of Quantum Mechanics. Additionally, we propose educational activities that introduce high school students to Quantum Mechanics by emphasizing entanglement as an essential concept to understand in order to become informed participants in the Second Quantum Revolution. Furthermore, we present the state-of-art developments of a largely unexplored and promising realization of real qubits, namely the molecular spin qubits. We review the available and suggested device architectures to host and use molecular spins. Moreover, we summarize the experimental findings on solid-state spin qubit devices based on magnetic molecules. Finally, we discuss how the Second Quantum Revolution might significantly transform law enforcement by offering specific examples and methodologies to address the evolving challenges in public safety and security. Full article

We investigate both theoretically and numerically the dynamics of out-of-time-ordered correlators (OTOCs) in quantum resonance conditions for a kicked rotor model. We employ various operators to construct OTOCs in order to thoroughly quantify their commutation relation at different times, therefore unveiling the process of quantum scrambling. With the help of quantum resonance condition, we have deduced the exact expressions of quantum states during both forward evolution and time reversal, which enables us to establish the laws governing OTOCs’ time dependence. We find interestingly that the OTOCs of different types increase in a quadratic function of time, breaking the freezing of quantum scrambling induced by the dynamical localization under non-resonance condition. The underlying mechanism is discovered, and the possible applications in quantum entanglement are discussed. Full article

Since the 1980s, researchers have taken giant steps in understanding how to use quantum mechanics for solving real problems—for example, making a computer that works according to the laws of quantum mechanics. In recent decades, researchers have tried to develop a platform for quantum information and computation that can be integrated into digital and telecom technologies without the need of a cryogenic environment. The current status of research in the field of quantum integrated photonics will be reviewed. A review of the most common integrated photonic platforms will be given, together with the main achievements and results in the last decade. Full article

Physicists are actively debating the nature of the quantum critical phase transition that determines the low-temperature properties of metals with heavy fermions. Important experimental observations of their transport properties incisively probe the nature of the quantum critical phase transition. In our short review, we consider the transport properties of strongly correlated Fermi systems like heavy fermion metals and high—$T_c$ superconductors. Their transport properties are defined by strong inter-particle interactions, forming flat bands in these compounds. These properties do not coincide with those of conventional metals. Indeed, in contrast to the behavior of the transport properties of conventional metals, the strongly correlated compounds exhibit linear temperature resistivity $\rho \left(T\right)\propto T$. We analyze the magnetoresistance and show that under the application of the magnetic field, it becomes negative. It is shown that near a quantum phase transition, when the density of the electronic states diverges, semiclassical physics remains applicable to describe the resistivity $\rho$ of strongly correlated metals due to the presence of a transverse zero-sound collective mode, representing the phonon mode in solids. We demonstrate that when T exceeds the extremely low Debye temperature $T_D$, the resistivity $\rho \left(T\right)$ changes linearly with T since the mechanism of formation of the T-dependence $\rho \left(T\right)$ is a similar electron-phonon mechanism, which predominates at high temperatures in ordinary metals. Thus, in the region of T-linear resistance, electron-phonon scattering leads to a lifetime of $\tau$ quasiparticles practically independent of the material, which is expressed as the ratio of the Planck constant ℏ to the Boltzmann constant $k_B$, $T\tau \sim \hslash /k_B$. We explain that due to the non-Fermi-liquid behavior, the real part of the frequency-dependent optical conductivity ${\sigma }_{opt}^R\left(\omega \right)$ exhibits a scaling behavior and demonstrates the unusual power law behavior ${\sigma }_{opt}^R\left(\omega \right)\propto {\omega }^{-1}$, rather than the well-known one shown by conventional metals, ${\sigma }_{opt}^R\left(\omega \right)\propto {\omega }^{-2}$. All our theoretical considerations are illustrated and compared with the corresponding experimental facts. Our results are in a good agreement with experimental observations. Full article

Counterfactual definiteness (CFD) means that if some property is measured in some context, then the outcome of the measurement would have been the same had this property been measured in a different context. A context includes all other measurements made together with the one in question, and the spatiotemporal relations among them. The proviso for CFD is non-disturbance: any physical influence of the contexts on the property being measured is excluded by the laws of nature, so that no one measuring this property has a way of ascertaining its context. It is usually claimed that in quantum mechanics CFD does not hold, because if one assigns the same value to a property in all contexts it is measured in, one runs into a logical contradiction, or at least contravenes quantum theory and experimental evidence. We show that this claim is not substantiated if one takes into account that only one of the possible contexts can be a factual context, all other contexts being counterfactual. With this in mind, any system of random variables can be viewed as satisfying CFD. The concept of CFD is closely related to but distinct from that of noncontextuality, and it is the latter property that may or may not hold for a system, in particular being contravened by some quantum systems. Full article

The review provides a pedagogical but comprehensive introduction to the foundations of a recently proposed statistical mechanics ($\mu$NEQT) of a stable nonequilibrium thermodynamic body, which may be either isolated or interacting. It is an extension of the well-established equilibrium statistical mechanics by considering microstates $\left\{{\mathfrak{m}}_k\right\}$ in an extended state space in which macrostates (obtained by ensemble averaging $\widehat{A}$) are uniquely specified so they share many properties of stable equilibrium macrostates. The extension requires an appropriate extended state space, three distinct infinitessimals $d_{\alpha }=(d,d_{\mathrm{e}},d_{\mathrm{i}})$ operating on various quantities q during a process, and the concept of reduction. The mechanical process quantities (no stochasticity) like macrowork are given by $\widehat{A}{d}_{\alpha }\mathsf{q}$, but the stochastic quantities ${\widehat{C}}_{\alpha }\mathsf{q}$ like macroheat emerge from the commutator ${\widehat{C}}_{\alpha }$ of $d_{\alpha }$ and $\widehat{A}$. Under the very common assumptions of quasi-additivity and quasi-independence, exchange microquantities $d_{\mathrm{e}}$q${}_k$ such as exchange microwork and microheat become nonfluctuating over $\left\{{\mathfrak{m}}_k\right\}$ as will be explained, a fact that does not seem to have been appreciated so far in diverse branches of modern statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.) that all use exchange quantities. In contrast, dq${}_k$ and $d_{\mathrm{i}}$q${}_k$ are always fluctuating. There is no analog of the first law for a microstate as the latter is a purely mechanical construct. The second law emerges as a consequence of the stability of the system, and cannot be violated unless stability is abandoned. There is also an important thermodynamic identity $d_{\mathrm{i}}Q\equiv d_{\mathrm{i}}W$$\ge 0$ with important physical implications as it generalizes the well-known result of Count Rumford and the Gouy-Stodola theorem of classical thermodynamics. The $\mu$NEQT has far-reaching consequences with new results, and presents a new understanding of thermodynamics even of an isolated system at the microstate level, which has been an unsolved problem. We end the review by applying it to three different problems of fundamental interest. Full article

This review presents the recent advances in the search for thermoelectric (TE) materials, mostly among intermetallic compounds and in the enhancement of their TE performance. Herein, contemporary approaches towards improving the efficiency of heat–electricity conversion (e.g., energy harvesting and heat pumping) are discussed through the understanding of various emergent physical mechanisms. The strategies for decoupling the individual TE parameters, as well as the simultaneous enhancement of the TE power factor and the suppression of heat conduction, are described for nanoparticle-doped materials, high entropy alloys, and nanowires. The achievement of a superior TE performance due to emergent quantum phenomena is discussed for intermetallic chalcogenides and related systems (e.g., strong and weak topological insulators, Weyl and Dirac semimetals), and some of the most promising compounds within these classes are highlighted. It was concluded that high-entropy alloying provides a methodological breakthrough for employing band engineering methods along with various phonon scattering mechanisms towards significant TE efficiency improvement in conventional TE materials. Finally, topological semimetals and magnetic semimetals with several intriguing features, such as a violation of the Wiedemann–Franz law and outstanding perpendicular Nernst signals, are presented as strong candidates for becoming next-generation TE quantum materials. Full article

In the field of nonlinear optics, quantum mechanics, condensed matter physics, and wave propagation in rigid and other nonlinear instability phenomena, the nonlinear Schrödinger equation has significant applications. In this study, the soliton solutions of the space-time fractional cubic nonlinear Schrödinger equation with Kerr law nonlinearity are investigated using an extended direct algebraic method. The solutions are found in the form of hyperbolic, trigonometric, and rational functions. Among the established solutions, some exhibit wide spectral and typical characteristics, while others are standard. Various types of well-known solitons, including kink-shape, periodic, V-shape, and singular kink-shape solitons, have been extracted here. To gain insight into the internal formation of these phenomena, the obtained solutions have been depicted in two- and three-dimensional graphs with different parameter values. The obtained solitons can be employed to explain many complicated phenomena associated with this model. Full article

Classical statistical mechanics has long relied on assumptions such as the equipartition theorem to understand the behavior of the complicated systems of many particles. The successes of this approach are well known, but there are also many well-known issues with classical theories. For some of these, the introduction of quantum mechanics is necessary, e.g., the ultraviolet catastrophe. However, more recently, the validity of assumptions such as the equipartition of energy in classical systems was called into question. For instance, a detailed analysis of a simplified model for blackbody radiation was apparently able to deduce the Stefan–Boltzmann law using purely classical statistical mechanics. This novel approach involved a careful analysis of a “metastable” state which greatly delays the approach to equilibrium. In this paper, we perform a broad analysis of such a metastable state in the classical Fermi–Pasta–Ulam–Tsingou (FPUT) models. We treat both the $\alpha$-FPUT and $\beta$-FPUT models, exploring both quantitative and qualitative behavior. After introducing the models, we validate our methodology by reproducing the well-known FPUT recurrences in both models and confirming earlier results on how the strength of the recurrences depends on a single system parameter. We establish that the metastable state in the FPUT models can be defined by using a single degree-of-freedom measure—the spectral entropy ($\eta$)—and show that this measure has the power to quantify the distance from equipartition. For the $\alpha$-FPUT model, a comparison to the integrable Toda lattice allows us to define rather clearly the lifetime of the metastable state for the standard initial conditions. We next devise a method to measure the lifetime of the metastable state $t_m$ in the $\alpha$-FPUT model that reduces the sensitivity to the exact initial conditions. Our procedure involves averaging over random initial phases in the plane of initial conditions, the $P_1$-$Q_1$ plane. Applying this procedure gives us a power-law scaling for $t_m$, with the important result that the power laws for different system sizes collapse down to the same exponent as $E{\alpha }^2\to 0$. We examine the energy spectrum $E\left(k\right)$ over time in the $\alpha$-FPUT model and again compare the results to those of the Toda model. This analysis tentatively supports a method for an irreversible energy dissipation process suggested by Onorato et al.: four-wave and six-wave resonances as described by the “wave turbulence” theory. We next apply a similar approach to the $\beta$-FPUT model. Here, we explore in particular the different behavior for the two different signs of $\beta$. Finally, we describe a procedure for calculating $t_m$ in the $\beta$-FPUT model, a very different task than for the $\alpha$-FPUT model, because the $\beta$-FPUT model is not a truncation of an integrable nonlinear model. Full article

Quantum chaos is reviewed from the viewpoint of “what is molecule?”, particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum electronic states provide potential functions working on nuclei, which in turn are often treated classically or semiclassically. Therefore, the classic study of chaos in molecular science began with those nuclear dynamics particularly about the vibrational energy randomization within a molecule. Statistical laws in probabilities and rates of chemical reactions even for small molecules of several atoms are among the chemical phenomena requiring the notion of chaos. Particularly the dynamics behind unimolecular decomposition are referred to as Intra-molecular Vibrational energy Redistribution (IVR). Semiclassical mechanics is also one of the main research fields of quantum chaos. We herein demonstrate chaos that appears only in semiclassical and full quantum dynamics. A fundamental phenomenon possibly giving birth to quantum chaos is “bifurcation and merging” of quantum wavepackets, rather than “stretching and folding” of the baker’s transformation and the horseshoe map as a geometrical foundation of classical chaos. Such wavepacket bifurcation and merging are indeed experimentally measurable as we showed before in the series of studies on real-time probing of nonadiabatic chemical reactions. After tracking these aspects of molecular chaos, we will explore quantum chaos found in nonadiabatic electron wavepacket dynamics, which emerges in the realm far beyond the Born-Oppenheimer paradigm. In this class of chaos, we propose a notion of Intra-molecular Nonadiabatic Electronic Energy Redistribution (INEER), which is a consequence of the chaotic fluxes of electrons and energy within a molecule. Full article