Search Results (42)

A classical fluid splitter produces the same patterns of energy redistribution as a Stern–Gerlach quantum device, with rotationally invariant coefficients of correlation between molecular paths. Alternative settings express a cosine squared relationship, leading to Tsirelson-type Bell violations with outcome independence. This result confirms the Correspondence Principle of quantum mechanics, where individual detection events express system-level properties according to Born’s Rule. Kochen–Specker contextuality and Bell Locality are not formally contradicted, but their interpretation is in question. Current definitions of “Local Realism” are limited to intrinsic particle properties. In contrast, quantum-like correlations require the acknowledgement of ensemble effects on dynamically inseparable entities, even when those entities are observed one at a time. Full article

We summarize our research program on the use of coherent states and covariant integral quantization in quantum cosmology. In particular, we present a recent development within this framework and include new results that shed light on some of its basic properties. Specifically, we investigate the quantum dynamics of a perturbed, fluid-filled Friedmann universe beyond the standard approximation in which the total state factorizes into background and perturbation wave functions. We assume the background geometry to be a superposition of two distinct coherent states—effectively a quantum cat state with no classical counterpart—each coupled to inhomogeneous perturbations. Starting from vacuum initial conditions, we analyze the evolution of a contracting universe through a bounce into the expanding phase. We find that an initially factorized state evolves into a biverse. This state consists of two distinct semiclassical branches, each described by a single coherent state and carrying enhanced perturbations in a slightly non-Gaussian state. We then explore how this dynamics depends on key model parameters, such as the perturbation wavelength and the choice of background solutions, and study their impact on the interaction between branches. The observed universe is assumed to correspond to one branch of this biverse state. This scenario illustrates how genuinely quantum properties of the background geometry may leave observable imprints in the early universe. Full article

We develop a unified Koopman–von Neumann (KvN) operator and Weyl–Wigner phase-space framework for inviscid ideal (barotropic) Euler flows. Our approach reformulates the nonlinear fluid dynamics as a linear KvN evolution on an enlarged field phase space, thereby enabling us to apply tools developed for quantum mechanics (Weyl quantization, Moyal ⋆-products, and Wigner functionals) to a classical fluid. We construct the appropriate KvN generator (including the required Jacobian term for unitarity) and derive the evolution equation for the corresponding Wigner functional. This framework clarifies when the classical Liouville (Vlasov) description is exact—namely, in quadratic or linear regimes where the Moyal bracket reduces to the Poisson bracket—and when higher-order quantum-like corrections become significant in fully nonlinear regimes. As an analytic example, we obtain a closed-form Wigner solution for a one-dimensional Burgers flow (pressureless Euler) and verify, term by term, that it reproduces the expected Liouville transport (with distributional contributions at the shock). We also compare the phase-space approach with a kinetic (Vlasov–monokinetic) formulation and outline the extension of the framework to three-dimensional flows using a Clebsch variable representation. Full article

We formulate a new quantum many-body simulation method for a general quantum fluid at any given temperature. Unlike the path integral Monte Carlo method, our method evolves, in imaginary time, the density matrix from its initial delta function condition to its final thermal form in an amount of time equal to the inverse temperature. It does this with a molecular dynamics scheme applied to a classical Hamiltonian that has the same functional form as the one for the quantum mechanical Hamiltonian according to the properties of the continuous representation of John R. Klauder. We then end up with the thermal density matrix, which can be used to extract thermal averages of observables using the Monte Carlo method equally well in any statistics. Full article

We briefly review the early development of the mean-field dynamics for cooperatively interacting quantum many-body systems, mapped to pseudo-spin (Ising-like) systems. We start with (Anderson, 1958) pseudo-spin mapping the BCS (1957) Hamiltonian of superconductivity, reducing it to a mean-field Hamiltonian of the XY (or effectively Ising) model in a transverse field. Then, we obtain the mean-field estimate for the equilibrium gap in the ground-state energy at different temperatures (gap disappearing at the transition temperature), which fits Landau’s (1949) phenomenological theory of superfluidity. We then present in detail a general dynamical extension (for non-equilibrium cases) of the mean-field theory of quantum Ising systems (in a transverse field), following de Gennes’ (1963) decomposition of the mean field into the orthogonal classical cooperative (longitudinal) component and the quantum (transverse) component, with each of the component following Suzuki–Kubo (1968) mean-field dynamics. Next, we discuss its applications to quantum hysteresis in Ising magnets (in the presence of an oscillating transverse field), to quantum heat engines (employing the transverse Ising model as a working fluid), and to the quantum annealing of the Sherrington–Kirkpatrick (1975) spin glass by tuning down (to zero) the transverse field, which provides us with a very fast computational algorithm, leading to ground-state energy values converging to the best-known analytic estimate for the model. Finally, we summarize the main results obtained and draw conclusions about the effectiveness of the de Gennes–Suzuki–Kubo mean-field equations for the study of various dynamical aspects of quantum condensed matter systems. Full article

The second virial coefficient (SVC) of the Lennard-Jones fluid is a cornerstone of molecular theory, yet its calculation has traditionally relied on the complex integration of the pair potential. This work introduces a fundamentally different approach by reformulating the problem in terms of ordinary differential equations (ODEs). For the classical component of the SVC, we generalize the confluent hypergeometric and Weber–Hermite equations. For the first quantum correction, we present entirely new ODEs and their corresponding exact-analytical solutions. The most striking result of this framework is the discovery that these ODEs can be transformed into Schrödinger-like equations. The classical term corresponds to a harmonic oscillator, while the quantum correction includes additional inverse-power potential terms. This formulation not only provides a versatile method for expressing the virial coefficient through a linear combination of functions (including Kummer, Weber, and Whittaker functions) but also reveals a profound and previously unknown mathematical structure underlying a classical thermodynamic property. Full article

Nearly homogeneous and isotropic turbulence, generated in flows through grids of various forms in wind tunnels or by towing or oscillating grids in stationary samples of classical viscous fluids and the superfluid phases of helium, have played an essential role in studies of the still partly unresolved problem of turbulence in fluids. This review describes a selected class of complementary grid experiments performed with classical viscous fluids such as air or water and with the superfluid liquid phases of ⁴He (He II) and ³He-B, which led to a deeper understanding of the underlying physics of turbulent quantum flows. In particular, we discuss the pioneering experiments on generating and probing quantum turbulence by oscillating grids in He II in the zero temperature limit, performed by Peter McClintock’s group in Lancaster. Full article

The basic structural concepts in the study of monatomic fluids at equilibrium are presented in this entry. The scope encompasses both the classical and the quantum domains, the latter concentrating on the diffraction and the zero-spin boson regimes. The main mathematical objects for describing the fluid structures are the following n-body functions: the correlation functions in real space and their associated structure factors in Fourier space. In these studies, the theory of linear response to external weak fields, involving functional calculus, and Feynman’s path integral formalism are the key conceptual ingredients. Emphasis is placed on the physical implications when going from the classical domain (limit of high temperatures) to the abovementioned quantum regimes (low temperatures). In the classical domain, there is only one class of n-body structures, which at every n level consists of one correlation function plus one structure factor. However, the quantum effects bring about the splitting of the foregoing class into three path integral classes, namely instantaneous, total thermalized-continuous linear response, and centroids; each of them is associated with the action of a distinct external weak field and keeps the above n-level structures. Special attention is given to the structural pair level $n=2$, and future directions towards the complete study of the quantum triplet level $n=3$ are suggested. Full article

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing an explicit quantum algorithm that implements the time evolution of a second-order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state with respect to the number of integration time-steps. This provides a significant improvement over previous approaches, while preserving the characteristic quantum speed-up in terms of the dimensionality of the underlying differential equations system, which similar time-marching quantum algorithms have previously demonstrated. Notably, by classically implementing the proposed algorithm, we showcase that it accurately captures the structural characteristics of the Lorenz system, reproducing both regular attractors–limit cycles–and the chaotic attractor within the chosen parameter regime. Full article

In earlier works, it was demonstrated that Schrödinger’s equation, which includes interactions with electromagnetic fields, can be derived from a fluid dynamic Lagrangian framework. This approach treats the system as a charged potential flow interacting with an electromagnetic field. The emergence of quantum behavior was attributed to the inclusion of Fisher information terms in the classical Lagrangian. This insight suggests that quantum mechanical systems are influenced not just by electromagnetic fields but also by information, which plays a fundamental role in driving quantum dynamics. This methodology was extended to Pauli’s equations by relaxing the constraint of potential flow and employing the Clebsch formalism. Although this approach yielded significant insights, certain terms remained unexplained. Some of these unresolved terms appear to be directly related to aspects of the relativistic Dirac theory. In a recent work, the analysis was revisited within the context of relativistic flows, introducing a novel perspective for deriving the relativistic quantum theory but neglecting the interaction with electromagnetic fields for simplicity. This is rectified in the current work, which shows the implications of the field in the current context. Full article

The current developments in the theory of quantum static triplet correlations and their associated structures (real r-space and Fourier k-space) in monatomic fluids are reviewed. The main framework utilized is Feynman’s path integral formalism (PI), and the issues addressed cover quantum diffraction effects and zero-spin bosonic exchange. The structures are associated with the external weak fields that reveal their nature, and due attention is paid to the underlying pair-level structures. Without the pair, level one cannot fully grasp the triplet extensions in the hierarchical ladder of structures, as both the pair and the triplet structures are essential ingredients in the triplet response functions. Three general classes of PI structures do arise: centroid, total continuous linear response, and instantaneous. Use of functional differentiation techniques is widely made, and, as a bonus, this leads to the identification of an exact extension of the “classical isomorphism” when the centroid structures are considered. In this connection, the direct correlation functions, as borrowed from classical statistical mechanics, play a key role (either exact or approximate) in the corresponding quantum applications. Additionally, as an auxiliary framework, the traditional closure schemes for triplets are also discussed, owing to their potential usefulness for rationalizing PI triplet results. To illustrate some basic concepts, new numerical calculations (path integral Monte Carlo PIMC and closures) are reported. They are focused on the purely diffraction regime and deal with supercritical helium-3 and the quantum hard-sphere fluid. Full article

Turbulence is the most important, ubiquitous, and difficult problem of classical physics. Feynman viewed it as essentially unsolved, without a rigorous mathematical basis to describe the statistical dynamics of this most complex of fluid motion. However, the paradigm shift came in 1959, with the formulation of the Eulerian direct interaction approximation (DIA) closure by Kraichnan. It was based on renormalized perturbation theory, like quantum electrodynamics, and is a bare vertex theory that is manifestly realizable. Here, we review some of the subsequent exciting achievements in closure theory and subgrid modelling. We also document in some detail the progress that has been made in extending statistical dynamical turbulence theory to the real world of interactions with mean flows, waves and inhomogeneities such as topography. This includes numerically efficient inhomogeneous closures, like the realizable quasi-diagonal direct interaction approximation (QDIA), and even more efficient Markovian Inhomogeneous Closures (MICs). Recent developments include the formulation and testing of an eddy-damped Markovian anisotropic closure (EDMAC) that is realizable in interactions with transient waves but is as efficient as the eddy-damped quasi-normal Markovian (EDQNM). As well, a similarly efficient closure, the realizable eddy-damped Markovian inhomogeneous closure (EDMIC) has been developed. Moreover, we present subgrid models that cater for the complex interactions that occur in geophysical flows. Recent progress includes the determination of complete sets of subgrid terms for skilful large-eddy simulations of baroclinic inhomogeneous turbulent atmospheric and oceanic flows interacting with Rossby waves and topography. The success of these inhomogeneous closures has also led to further applications in data assimilation and ensemble prediction and generalization to quantum fields. 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

In this paper we would like to highlight the problems of conceiving the “Hydrogen Bond” (HB) as a real short-range, directional, electrostatic, attractive interaction and to reframe its nature through the non-approximated view of condensed matter offered by a Quantum Electro-Dynamic (QED) perspective. We focus our attention on water, as the paramount case to show the effectiveness of this 40-year-old theoretical background, which represents water as a two-fluid system (where one of the two phases is coherent). The HB turns out to be the result of the electromagnetic field gradient in the coherent phase of water, whose vacuum level is lower than in the non-coherent (gas-like) fraction. In this way, the HB can be properly considered, i.e., no longer as a “dipolar force” between molecules, but as the phenomenological effect of their collective thermodynamic tendency to occupy a lower ground state, compatible with temperature and pressure. This perspective allows to explain many “anomalous” behaviours of water and to understand why the calculated energy associated with the HB should change when considering two molecules (water-dimer), or the liquid state, or the different types of ice. The appearance of a condensed, liquid, phase at room temperature is indeed the consequence of the boson condensation as described in the context of spontaneous symmetry breaking (SSB). For a more realistic and authentic description of water, condensed matter and living systems, the transition from a still semi-classical Quantum Mechanical (QM) view in the first quantization to a Quantum Field Theory (QFT) view embedded in the second quantization is advocated. Full article

The quantum Wigner function and non-equilibrium equation for a microscopic particle in one spatial dimension ($1D$) subject to a potential and a heat bath at thermal equilibrium are considered by non-trivially extending a previous analysis. The non-equilibrium equation yields a general hierarchy for suitable non-equilibrium moments. A new non-trivial solution of the hierarchy combining the continued fractions and infinite series thereof is obtained and analyzed. In a short thermal wavelength regime (keeping quantum features adequate for chemical reactions), the hierarchy is approximated by a three-term one. For long times, in turn, the three-term hierarchy is replaced by a Smoluchovski equation. By extending that $1D$ analysis, a new model of the growth (polymerization) of a molecular chain (template or $te$) by binding an individual unit (an atom) and activation by a catalyst is developed in three spatial dimensions ($3D$). The atom, $te$, and catalyst move randomly as solutions in a fluid at rest in thermal equilibrium. Classical statistical mechanics describe the $te$ and catalyst approximately. Atoms and bindings are treated quantum-mechanically. A mixed non-equilibrium quantum–classical Wigner–Liouville function and dynamical equations for the atom and for the $te$ and catalyst, respectively, are employed. By integrating over the degrees of freedom of $te$ and with the catalyst assumed to be near equilibrium, an approximate Smoluchowski equation is obtained for the unit. The mean first passage time (MFPT) for the atom to become bound to the $te$, facilitated by the catalyst, is considered. The resulting MFPT is consistent with the Arrhenius formula for rate constants in chemical reactions. Full article