We develop a theoretical framework for describing superposed coherent states in graphene quantum systems using the concept of catability as a phase-sensitive metric functional measure. In this case, the formalism quantifies interference stability and coherence structure via phase-dependent contributions of quantum superposition states. Catability is defined as a functional measure sensitive to relative phase variations within coherent state combinations, serving as a diagnostic tool for quantum interference effects in graphene-based systems. Also, the formulation is extended using Lie algebra techniques, where the underlying symmetry structure of graphene quantum states is represented through operator algebras governing state transformations in quantum space. In this context, to describe nonlocal propagation and phase-resolved dynamics, a Green function approach is incorporated, enabling systematic treatment of quantum correlations in a spatially extended structures framework. A unified framework is constructed by combining Lie algebraic symmetry analysis with Green function propagation theory, yielding a consistent description of phase-sensitive catability in complex graphene quantum configurations within the framework approach. Results provide a structured route for testing coherence, interference stability, and quantum state control in low-dimensional quantum materials systems.
Testing Catability and Coherent Superposition of 2D Graphene Quantum system
We develop a theoretical framework for describing superposed coherent states in graphene quantum systems using the concept of catability as a phase-sensitive metric functional measure. In this case, the formalism quantifies interference stability and coherence structure via phase-dependent contributions of quantum superposition states. Catability is defined as a functional measure sensitive to relative phase variations within coherent state combinations, serving as a diagnostic tool for quantum interference effects in graphene-based systems. Also, the formulation is extended using Lie algebra techniques, where the underlying symmetry structure of graphene quantum states is represented through operator algebras governing state transformations in quantum space. In this context, to describe nonlocal propagation and phase-resolved dynamics, a Green function approach is incorporated, enabling systematic treatment of quantum correlations in a spatially extended structures framework. A unified framework is constructed by combining Lie algebraic symmetry analysis with Green function propagation theory, yielding a consistent description of phase-sensitive catability in complex graphene quantum configurations within the framework approach. Results provide a structured route for testing coherence, interference stability, and quantum state control in low-dimensional quantum materials systems.
In this work, a unified Lie-algebraic formulation of catability is constructed for relativistic quantum systems with arbitrary spin within this framework. In this case, the analysis starts with constructing catability as a quantitative measure for superposed coherent states, where coherence structure and quantum interference properties are studied using algebraic representations in this framework. Also, a generalized Foldy-Wouthuysen transformation is formulated within a Lie algebraic framework, delivering a systematic procedure for block-diagonalization of relativistic Hamiltonians and separation of positive- and negative-energy components in this framework. Within this formalism, a phase-sensitive catability operator is introduced to study phase correlations and coherence effects in the relativistic quantum dynamics framework. The approach is applied to Dirac spin-1/2 particles, where relativistic fermionic catability is analyzed in relation to spinorial structures and symmetry generators framework. The formalism is extended through a unified geometric and Lie-algebraic treatment, establishing a consistent description of catability in a relativistic quantum mechanics framework. In this context, the generalized framework is constructed for arbitrary spin-s fields, enabling investigation of higher-spin relativistic quantum states within the same algebraic structure framework. In this context, the obtained results show a generalized theoretical platform for investigating relativistic quantum coherence, superposition effects, and algebraic symmetries in the framework of fermionic and bosonic systems.
We develop a unified framework for studying superposed coherent states in coupled nonlinear bosonic systems using a q-deformed Kerr oscillator model. A quantitative measure, termed catability, is introduced to quantify robustness and structural coherence of Schrödinger-cat-like states under nonlinear and deformation effects within the framework. Within the q-deformed bosonic algebra, we analyze the dynamics of two coupled Kerr oscillators to demonstrate that the deformation parameter governs coherence redistribution and nonlinear coupling-induced state transformation. Establish local cat states emerge from the relation between Kerr nonlinearity and q-deformed interactions, coherence transfer between subsystems becomes sensitive to the deformation strength. In this case, construct a phase diagram of catability, revealing distinct regimes of quantum behavior, identifying coupling-driven quantum phase transitions in a deformed algebraic structure system. The generalized analysis extended the covariant formulation and graphene-inspired catability operators generalized curved space-time backgrounds, establishing a connection between nonlinear quantum optics, condensed matter analog systems, relativistic quantum structures framework. In this context, results explain complete description deformationcontrolled quantum coherence and establish new directions for engineered nonclassical states in complex quantum systems.
Quantum coherence lies at the heart of quantum mechanics and underlies interference, entanglement, and quantum information. Within conventional quantum theory, coherence is mathematically represented by the wavefunction or, more generally, by the off-diagonal elements of the density matrix. Although this formalism predicts experimental observations with extraordinary precision, the physical origin of coherence and its apparent disappearance during measurement continue to motivate diverse interpretations, including the Copenhagen interpretation, decoherence theory, many-worlds, relational quantum mechanics, and QBism. In the present work we propose a complementary structural interpretation based on Green-Function Architecture Theory (GFAT). Rather than considering quantum coherence to be a primitive property of the wavefunction, we propose that coherence is fundamentally a property of connected Green-function architectures represented by diagram spaces. The wavefunction is interpreted as an effective Hilbert-space representation of an underlying Green-function architecture. Within this framework, quantum interference arises from architecture coherence associated with a common holonomy, whereas measurement corresponds to an architecture transformation that redistributes coherence without destroying it. Consequently, wavefunction collapse is interpreted as an emergent description of a deeper structural process occurring within the underlying Green-function architecture. The proposed framework leaves the mathematical predictions of quantum mechanics completely unchanged while suggesting a deeper structural origin for quantum coherence, interference, and measurement. The double-slit experiment is discussed as the first physical application of this architecture-based interpretation.
Although the principle of superposition lies at the heart of quantum mechanics and is the root of almost all quantum phenomena such as coherence and entanglement, its quantification, except for that related to the resource theory of coherence and interference, remains relatively less studied. In this work, we address quantification of superposition from an information-theoretic perspective. We introduce a family of quantifiers of superposition, the phase-sensitive superposition, by taking into account the phases of amplitudes in the superposition of a fixed basis states (e.g., computational basis states). We establish a conservation relation for the phase-sensitive superposition, which is a kind of complementary relation and is reminiscent of wave-particle duality. We evaluate explicitly the second moment of phase-sensitive superposition and show that it is intrinsically related to the l2-norm coherence. We characterize the dephasing channel induced by the maximally superposed states. We investigate the minimum and maximum superpositions, reveal their basic properties, and illustrate them through various examples. We further explore the dynamics of superposition in the Grover search algorithm, and demonstrate a complementary relation between superposition and success probability of the search algorithm. These results and quantifiers offer tools for analyzing structural features and implications of quantum superposition.
Quantum mechanics provides one of the most accurate mathematical descriptions of Nature, successfully explaining interference, superposition, entanglement, quantum measurement, and the dynamics of microscopic systems. Despite its remarkable predictive success, the physical origin of quantum coherence and the interpretation of wavefunction collapse remain subjects of ongoing debate, leading to numerous interpretations including the Copenhagen interpretation, decoherence theory, the many-worlds interpretation, relational quantum mechanics, and QBism. In this work we propose Green-Function Architecture Theory (GFAT) as a structural framework underlying the conventional Hilbert-space formulation of quantum mechanics. Rather than modifying the mathematical formalism of quantum theory, GFAT introduces a deeper structural level based upon interacting Green functions and their associated diagram spaces. Within this framework, quantum coherence is proposed to be a property of connected Green-function architectures, while wavefunctions are interpreted as effective Hilbert-space representations reconstructed from these architectures. The framework introduces three structural principles: the Architecture Coherence Principle, the Architecture Representation Principle, and the Architecture Conservation Principle. These principles provide a unified structural interpretation of quantum interference, measurement, decoherence, geometric phases, entanglement, bound states, and particle stability. Existing interpretations of quantum mechanics are not regarded as competing descriptions but as complementary mathematical layers representing the same underlying physical reality. The present work therefore proposes a structural foundation of quantum physics in which Green-function architectures provide the underlying organizational principle from which quantum phenomena emerge while leaving
We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A 31, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical systems possessing Lie-group symmetries. The concept of generalized coherent states and the method of harmonic analysis are used to construct explicitly a family of phase-space functions which are postulated to satisfy the Stratonovich-Weyl correspondence with a generalized tracing condition. The symbol calculus for the phase-space functions is given by means of the generalized twisted product. The phase-space formalism is used to study the problem of the reconstruction of quantum states. In particular, we consider the reconstruction method based on measurements of displaced projectors, which comprises a number of recently proposed quantum-optical schemes and is also related to the standard methods of signal processing. A general group-theoretic description of this method is developed using the technique of harmonic expansions on the phase space.