Dongwoo Kwak

Wave Incommensurability as the Dynamical Origin of Quantum Spectral Rigidity and Orbital Stability: From the Montgomery–Dyson Correspondence to Semiclassical Orbit Selection

The 50-year-old Montgomery–Dyson correspondence, R₂(r) = 1 − (sin(πr) / (πr))² ≡ R₂(u) is neither a numerical coincidence nor an abstract random-matrix postulate. We identify the quantum spectral spacing variable r as an incommensurate transition beat frequency ratio (r ∉ ℤ). In...

Wave Incommensurability as the Dynamical Origin of Quantum Spectral Rigidity and Orbital Stability: From the Montgomery–Dyson Correspondence to Semiclassical Orbit Selection

The 50-year-old Montgomery–Dyson correspondence, R₂(r) = 1 − (sin(πr) / (πr))² ≡ R₂(u) is neither a numerical coincidence nor an abstract random-matrix postulate. We identify the quantum spectral spacing variable r as an incommensurate transition beat frequency ratio (r ∉ ℤ). In...

Dynamical Origin of Spectral Rigidity and the Montgomery–Dyson Correspondence: Part II. Controlled Commensurate Transition of Nuclear Level Statistics

In Part I, we proposed that quantum spectral level repulsion is dynamically sustained by continuous wave-node incommensurability, whereby non-divisible transition beat frequencies suppress harmonic phase locking. Here, we test this mechanism through a baseline-and-inverse-interve...

Dynamical Origin of Spectral Rigidity and the Montgomery–Dyson Correspondence: Part III. Semiclassical Orbit Selection Hypothesis and Wave-Dynamical Interference in the Gutzwiller Trace Formula

While the Montgomery–Dyson correspondence revealed a statistical equivalence between the non-trivial zeros of the Riemann zeta function and complex quantum spectra, its microscopic dynamical origin remains an open question. In semiclassical physics, the Gutzwiller trace formula r...

Dynamical Origin of Spectral Rigidity and the Montgomery–Dyson Correspondence: Part III. Semiclassical Orbit Selection Hypothesis and Wave-Dynamical Interference in the Gutzwiller Trace Formula

While the Montgomery–Dyson correspondence revealed a statistical equivalence between the non-trivial zeros of the Riemann zeta function and complex quantum spectra, its microscopic dynamical origin remains an open question. In semiclassical physics, the Gutzwiller trace formula r...

Dynamical Origin of Spectral Rigidity and the Montgomery–Dyson Correspondence: Part II. Controlled Commensurate Transition of Nuclear Level Statistics

In Part I, we proposed that quantum spectral level repulsion is dynamically sustained by continuous wave-node incommensurability—the non-divisibility of transition beat frequencies suppressing harmonic resonance locking. Here, we provide controlled numerical evidence through a tw...

Dynamical Origin of Spectral Rigidity and the Montgomery–Dyson Correspondence: Part II. Controlled Commensurate Transition of Nuclear Level Statistics

In Part I, we proposed that quantum spectral level repulsion is dynamically sustained by continuous wave-node incommensurability, whereby non-divisible transition beat frequencies suppress harmonic phase locking. Here, we test this mechanism through a baseline-and-inverse-interve...

Dynamical Origin of Spectral Rigidity and the Montgomery–Dyson Correspondence: Part II. Controlled Commensurate Transition of Nuclear Level Statistics

In Part I, we proposed that quantum spectral level repulsion is dynamically sustained by continuous wave-node incommensurability—the non-divisibility of transition beat frequencies suppressing harmonic resonance locking. Here, we provide controlled numerical evidence through a tw...

Dynamical Origin of Spectral Rigidity and the Montgomery–Dyson Correspondence: Part III. Semiclassical Orbit Selection Hypothesis and Wave-Dynamical Interference in the Gutzwiller Trace Formula

While the Montgomery–Dyson correspondence revealed a profound statistical equivalence between the non-trivial zeros of the Riemann zeta function and complex quantum spectra, its microscopic dynamical origin remains an open question. In semiclassical physics, the Gutzwiller trace...

Dynamical Origin of Spectral Rigidity and the Montgomery–Dyson Correspondence: Part II. Controlled Commensurate Transition of Nuclear Level Statistics

In Part I, we proposed that quantum spectral level repulsion can naturally emerge from continuous wave-node incommensurability—the dynamical non-divisibility of transition beat frequencies that suppresses harmonic resonance locking. In this companion paper (Part II), we provide c...

Dynamical Origin of Spectral Rigidity and the Montgomery–Dyson Correspondence: Part II. Controlled Commensurate Transition of Nuclear Level Statistics

For over half a century following the 1973 encounter between Hugh Montgomery and Freeman Dyson, the matching pair-correlation statistics governing the non-trivial zeros of the Riemann zeta function and the eigenvalues of random matrix ensembles have presented a profound, unresolv...

Continuous Wave Incommensurability over Primes: Dynamical Level Repulsion, Finite-Time Resonance Avoidance, and the Physical Origin of Spectral Rigidity

Since the Montgomery–Dyson encounter, the correspondence between Riemann zeta zeros and quantum spectral statistics has motivated efforts to identify a bridge between arithmetic structure and physical spectra. However, microscopic quantum transition frequencies reflect continuous...

Continuous Wave Incommensurability over Primes: Dynamical Level Repulsion, Finite-Time Resonance Avoidance, and the Physical Origin of Spectral Rigidity

Since the Montgomery–Dyson encounter, the correspondence between Riemann zeta zeros and quantum spectral statistics has motivated efforts to identify a bridge between arithmetic structure and physical spectra. However, microscopic quantum transition frequencies reflect continuous...

Continuous Wave Incommensurability over Primes: Dynamical Level Repulsion, Finite-Time Resonance Avoidance, and the Physical Origin of Spectral Rigidity

For over fifty years following the Montgomery–Dyson encounter, the correspondence between the non-trivial zeros of the Riemann zeta function and quantum spectral statistics has motivated attempts to identify a deeper connection between arithmetic structure and quantum spectra. Th...

Continuous Wave Incommensurability over Primes: Dynamical Level Repulsion, Finite-Time Resonance Avoidance, and the Physical Origin of Spectral Rigidity

For over fifty years, the Montgomery–Dyson correspondence has posed an unresolved enigma: why do the non-trivial zeros of the Riemann zeta function and random Hermitian matrix eigenvalues share the identical pair correlation function, R_2(s) = 1 - (sin(pi*s)/(pi*s))^2? Mainstream...

Continuous Wave Incommensurability over Primes: Dynamical Level Repulsion, Finite-Time Resonance Avoidance, and the Physical Origin of Spectral Rigidity

For over fifty years following the Montgomery–Dyson encounter, the correspondence between the non-trivial zeros of the Riemann zeta function and quantum spectral statistics has motivated extensive investigation into the relation between arithmetic structure and quantum spectra. T...

Continuous Wave Incommensurability over Primes: Dynamical Level Repulsion, Finite-Time Resonance Avoidance, and the Physical Origin of Spectral Rigidity

For over fifty years following the Montgomery–Dyson encounter, the correspondence between the non-trivial zeros of the Riemann zeta function and quantum spectral statistics has motivated extensive investigation into the relation between arithmetic structure and quantum spectra. T...

Radiation Beat Frequency Incommensurability: Resolving Quantum Level Repulsion and Riemann-Type Spectral Rigidity via Finite-Shell (n ≤ 8) Orbit Ratios (1/n²)

For over half a century since the historic encounter between Montgomery and Dyson, the exact correspondence between the pair correlation of non-trivial Riemann zeta zeros and the eigenvalue spacing statistics of complex quantum systems has remained an open foundational puzzle—fre...

Radiation Beat Frequency Incommensurability: Resolving Quantum Level Repulsion and Riemann-Type Spectral Rigidity via Finite-Shell (n ≤ 8) Orbit Ratios (1/n²)

For over half a century since the historic encounter between Montgomery and Dyson, the exact correspondence between the pair correlation of non-trivial Riemann zeta zeros and the eigenvalue spacing statistics of complex quantum systems has remained an open foundational puzzle—fre...

Demythologizing Spectral Rigidity and Level Repulsion Statistics via Algebraic Incommensurability in Finite Quantum Shells: A Deterministic Framework Based on Non-Integer Multiplicity of Inter-Shell Beat Frequencies

The striking structural identity between the 2-point pair correlation function of the non-trivial zeros of the Riemann zeta function $R_2(r) = 1 - \left(\frac{\sin(\pi r)}{\pi r}\right)^2$ and the energy level spacing statistics of complex quantum systems has long been framed as...