Search Results (64)

This article discusses the quantization of linear Hamiltonian systems, a historically rich but under explored line of research. The key idea is that a classical linear Hamiltonian system induces on its phase space a compatible complex structure and scalar product, giving rise to a complex Hilbert space where classical dynamics becomes a one-parameter unitary group. Boson Fock quantization of this group then recovers, up to unitary equivalence, the results of canonical quantization. This expository overview traces the development of this framework from foundational works to modern symplectic perspectives, offering a case study in the dialogue between analysis, geometry, and physics. Full article

We develop a digitization-based analysis workflow for characterizing the entropy and correlation structure of truncated bosonic quantum fields after embedding them into small qubit registers, and illustrate it on the steady state of a coherently pumped micromaser. The cavity field is truncated to 32 Fock levels and embedded into a five-qubit register via a Gray-code mapping of photon number to computational basis states, with binary encoding used as a benchmark. On this register we compute reduced entropies, mutual informations, bipartite negativities and Coffman–Kundu–Wootters three-tangles for all qubit pairs and triplets, and use the resulting patterns to define information graphs. The micromaser Liouvillian naturally supports trapping manifolds in Fock space, whose structure depends on the choice of interaction angle and on thermal coupling to the reservoir. We show that these manifolds leave a clear imprint on the digitized information graph: multi-block trapping configurations induce sparse, banded patterns dominated by a few two-qubit links, while trapping on a single 32-dimensional manifold or coupling to a thermally populated cavity leads to more delocalized and collectively shared correlations. The entropy and mutual-information profiles of the register provide a complementary view on how energy and information are distributed across qubits in different parameter regimes. Although the full micromaser dynamics can in principle generate higher-order entanglement, we focus here on well-defined measures of two- and three-party correlations and treat the emerging information graph as a structural probe of digitized field states. We expect the workflow to transfer to other bosonic fields encoded in small qubit registers, and outline how the resulting information-graph view can serve as a practical diagnostic in studies of driven-dissipative correlation structure. Full article

We extend the classical fractal uncertainty principle (FUP) framework in time-frequency analysis by exploring several novel directions. First, we generalize the FUP beyond the classical Gaussian window by investigating non-Gaussian windows and the corresponding generalized Fock space techniques. Second, we develop uncertainty estimates in alternative joint representations, including the continuous wavelet transform and directional representations such as shearlets. Third, we study fractal uncertainty on random and anisotropic fractal sets, providing probabilistic and geometric refinements of the FUP. Fourth, we connect these results with semiclassical and microlocal analysis, thereby elucidating the role of fractal geometry in resonance theory and pseudodifferential operators. Finally, we extend the analysis beyond Gaussian Gabor multipliers by considering non-Gaussian generating functions and irregular lattice samplings. Our results yield new operator norm estimates and spectral properties, with potential applications in signal processing, quantum mechanics, and numerical analysis. Full article

We generalize our recent work on k-essence sourcing Kerr–Schild spacetimes to the kinetic gravity braiding scalar field. For k-essence, in order for a perturbative Kerr–Schild-type solution to become exact, the k-essence Lagrangian must either be linear in the kinetic term (with the Kerr–Schild congruence autoparallel) or unrestricted, provided the scalar gradient along the congruence vanishes. A similar reasoning for the pure kinetic braiding contribution leads to either a vanishing Lagrangian or a scalar that is constant along the congruence. From the scalar dynamics we also derive an accompanying constraint. Finally, we discuss pp-waves, an example of Kerr–Schild spacetime generated by a constant k-essence along the Kerr–Schild congruence with a vanishing Lagrangian. This allows for the construction of a Fock-type space, consisting of a tower of Kerr–Schild maps first yielding a vacuum pp-wave from flat spacetime; next a k-essence-generated pp-wave from the vacuum pp-wave; and finally an arbitrary number of k-essence pp-waves with different retarded time-dependent metric functions. Full article

In the present scenario, coherent states of a quantum harmonic oscillator are generalized with positive Fox H auxiliary functions. The novel generalized coherent states provide canonical coherent states and Mittag-Leffler or Wright generalized coherent states, as particular cases, and resolve the identity operator, over the Fock space, with a weight function that is the product of a Fox H function and a Wright generalized hypergeometric function. The novel generalized coherent states, or the corresponding truncated generalized coherent states, are characterized by anomalous statistics for large values of the number of excitations: the corresponding decay laws exhibit, for determined values of the involved parameters, various behaviors that depart from exponential and inverse-power-law decays, or their product. The analysis of the Mandel Q factor shows that, for small values of the label, the statistics of the number of excitations becomes super-Poissonian, or sub-Poissonian, by simply choosing sufficiently large values of one of the involved parameters. The time evolution of a generalized coherent state interacting with a thermal reservoir and the purity are analyzed. Full article

This paper presents a mathematical formalism for generative artificial intelligence (GAI). Our starting point is an observation that a “histories” approach to physical systems agrees with the compositional nature of deep neural networks. Mathematically, we define a GAI system as a family of sequential joint probabilities associated with input texts and temporal sequences of tokens (as physical event histories). From a physical perspective on modern chips, we then construct physical models realizing GAI systems as open quantum systems. Finally, as an illustration, we construct physical models realizing large language models based on a transformer architecture as open quantum systems in the Fock space over the Hilbert space of tokens. Our physical models underlie the transformer architecture for large language models. Full article

We present a simple argument to derive the transformation of the quantum stochastic calculus formalism between inertial observers and derive the quantum open system dynamics for a system moving in a vacuum (or, more generally, a coherent) quantum field under the usual Markov approximation. We argue, however, that, for uniformly accelerated open systems, the formalism must break down as we move from a Fock representation over the algebra of field observables over all of Minkowski space to the restriction regarding the algebra of observables over a Rindler wedge. This leads to quantum noise having a unitarily inequivalent non-Fock representation: in particular, the latter is a thermal representation at the Unruh temperature. The unitary inequivalence is ultimately a consequence of the underlying flat noise spectrum approximation for the fundamental quantum stochastic processes. We derive the quantum stochastic limit for a uniformly accelerated (two-level) detector and establish an open system description of the relaxation to thermal equilibrium at the Unruh temperature. Full article

The electronic structures of the first- and second-row homonuclear diatomics, XeF₂, and the weakly bound dimers of nitric oxide and nitrogen dioxide molecules in their ground states are discussed in terms of molecular orbital (MO) theory and, where possible, valence bond theories. The current work is extended and supported by restricted and unrestricted Hartree–Fock (RHF and UHF) self-consistent field (SCF), complete active space SCF (CASSCF), multi-reference configuration interaction (MRCI), coupled cluster CCSD(T), and unrestricted Kohn–Sham (UKS) density functional calculations using a polarized triple-zeta basis. The dicarbon (C₂) molecule is especially poorly described by RHF theory, and it is argued that the current MO theories taught in most undergraduate courses should be extended in recognition of the fact that the molecule requires at least a two-configuration treatment. Full article

Before we ask what the quantum gravity theory is, there is a legitimate quest to formulate a robust quantum field theory in curved spacetime (QFTCS). Several conceptual problems, especially unitarity loss (pure states evolving into mixed states), have raised concerns over several decades. In this paper, acknowledging the fact that time is a parameter in quantum theory, which is different from its status in the context of General Relativity (GR), we start with a “quantum first approach” and propose a new formulation for QFTCS based on the discrete spacetime transformations which offer a way to achieve unitarity. We rewrite the QFT in Minkowski spacetime with a direct-sum Fock space structure based on the discrete spacetime transformations and geometric superselection rules. Applying this framework to QFTCS, in the context of de Sitter (dS) spacetime, we elucidate how this approach to quantization complies with unitarity and the observer complementarity principle. We then comment on understanding the scattering of states in de Sitter spacetime. Furthermore, we discuss briefly the implications of our QFTCS approach to future research in quantum gravity. Full article

There are two aims in this paper. The first aim is to characterize the order-bounded weighted composition operators between Fock spaces, and the second is to further characterize the order-bounded difference in weighted composition operators between Fock spaces. At the same time, six examples are given to illustrate the relations between boundedness and ordered boundedness. Moreover, an interesting result is found that differences in weighted composition operators defined by some special weighted functions and symbol functions are order-bounded between Fock spaces if and only if each weighted composition operator is compact between Fock spaces. Finally, two open questions are also put forward for converting larger Fock spaces into smaller ones. Full article

One aim of the paper is to characterize some complex symmetric and 2-complex symmetric bounded weighted superposition operators on Fock spaces respect to the conjugations $\mathcal{J}$ and ${\mathcal{J}}_{r,s,t}$ defined by $\mathcal{J}f\left(z\right)=\overline{f\left(\overline{z}\right)}$ and ${\mathcal{J}}_{r,s,t}f\left(z\right)=t{e}^{sz}\overline{f\left(\overline{rz+s}\right)}$. Another aim is to characterize the order bounded weighted superposition operators from one Fock space into another Fock space. Full article

The potential energy curves (PECs) and spectroscopic constants of the ground and excited states of a LiMg⁺ molecular cation were investigated. We obtained accurate results for the fifteen lowest-lying states of the LiMg⁺ cation using the Intermediate Hamiltonian Fock Space Multireference Coupled Cluster (IH-FS-CC) method applied to the (2,0) sector. Relativistic corrections were accounted for using the third-order Douglas–Kroll method. In each instance, smooth PECs were successfully computed across the entire range of interatomic distances from equilibrium to the dissociation limit. The results are in good accordance with previous studies of this molecular cation. Notably, this study marks the first application of IH-FS-CC in investigating a mixed alkali and alkaline earth molecular cation, proving its usability in determining accurate PECs of such diatomics and their spectroscopic constants. Full article

We characterize the boundedness and compactness of dual Toeplitz operators on the orthogonal complement of the generalized Fock space. We study the problem when the finite sum of the dual Toeplitz products is compact. Additionally, we also consider when the sum of the dual Toeplitz operators is equal to another dual Toeplitz operator. Full article

In this paper, we update the phase-space factors for all two-neutrino double electron capture processes. The Dirac–Hartree–Fock–Slater self-consistent method is employed to describe the bound states of captured electrons, enabling a more realistic treatment of atomic screening and more precise binding energies of the captured electrons compared to previous investigations. Additionally, we consider all s-wave electrons available for capture, expanding beyond the K and $L_1$ orbitals considered in prior studies. For light atoms, the increase associated with additional captures compensates for the decrease in decay rate caused by the more precise atomic screening. However, for medium and heavy atoms, an increase in the decay rate, up to 10% for the heaviest atoms, is observed due to the combination of these two effects. In the systematic analysis, we also include capture fractions for the first few dominant partial captures. Our precise model enables a close examination of low Q-value double electron capture in ¹⁵²Gd, ¹⁶⁴Er, and ²⁴²Cm, where partial $KK$ captures are energetically forbidden. Finally, with the updated phase-space values, we recalculate the effective nuclear matrix elements and compare their spread with those associated with $2\nu {\beta }^{-}{\beta }^{-}$ decay. Full article