Microscopic Currents Are Easily Self Sustaining

——A Unified Picture from Confined Spectrum, Coherent Frequency Locking to Topological Protection

I. The Fundamental Divide Between Macroscopic Dissipation and Microscopic Persistence

Currents in macroscopic conductors usually decay exponentially, rooted in strong decoherence and openness:

• Coherence length is much smaller than the system size: electrons frequently scatter off phonons, impurities, and boundaries during propagation;

• Abundant energy channels: momentum is continuously converted into thermal energy, with the system strongly coupled to the "heat bath";

• No global phase constraint: currents lack a unified quantum phase and cannot form a steady state.

In contrast, microscopically confined systems (such as atoms, small molecular rings, and mesoscopic rings) can support nearly permanent non-dissipative currents, due to a triple protection mechanism:

• Size smaller than the coherence length: the entire system lies within the quantum coherent domain;

• Weak environmental coupling: energy exchange between the ground state (or low-excited states) and the external environment is extremely weak;

• Eigenstates are non-radiative: once occupying a stationary state, the system evolves with a single phase factor, charge density does not change with time, the time-averaged Poynting vector is zero, and there is no net electromagnetic radiation.

In other words: Microscopic currents do not vanish not because they are driven, but because they have "settled" in a self-consistent, closed, non-dissipative eigenstate.

II. "Spectrum Frequency Closing" and "Natural Frequency Locking": The Mathematical Root of Stability

Any confined system—whether a string, cavity, or atomic orbital—will "close" the continuous spectrum into discrete eigenmodes due to boundary or potential well constraints. This process can be called "frequency closing."

• At these discrete frequency points, the system can form standing wave resonance;

• If the system is in an energy eigenstate ψₙ(r)e⁻ⁱᴱₙᵗ/ℏ, its probability density |ψ|² does not change with time;

• Despite the presence of non-zero current density:j(r) = (eℏ/m)Im[ψ*∇ψ] − (e²/m)|ψ|²A,it satisfies ∂ρ/∂t = 0 and ∇⋅j = 0, forming a steady-state circulation;

• Due to the static charge distribution, far-field radiation cancels out, and the system is in a non-radiative steady state.

This is the physical basis for "perpetual currents" such as atomic orbital magnetic moments and electron spins—they are not the result of dynamic equilibrium, but a direct manifestation of spectral discreteness and phase coherence.

III. Energy Gap and Topology: Double Barriers Against Decay

Even in the presence of perturbations, microscopic circulations are difficult to decay continuously, for two reasons:

• Energy gap protection: Many microscopic steady states (such as superconducting paired states, atomic ground states) have an excitation energy gap; breaking the circulation requires crossing the energy barrier, with extremely low probability;

• Topological/quantization constraints: The single-valuedness of the wavefunction requires that the phase recovers after circling a closed path, i.e.,∮∇θ⋅dl = 2πn, n∈Z.

This leads to flux quantization and angular momentum quantization, "locking" the circulation intensity into discrete values that cannot slide smoothly to zero.

These "integer barriers" endow microscopic circulations with robustness: perturbations can only induce transitions (if energy is sufficient) but cannot smoothly erase the current.

IV. Three Typical Manifestations of Microscopic Steady Currents

Atomic Stationary Currents

Electrons in atomic orbitals form closed circulations, generating orbital magnetic moments; spin can be understood as intrinsic vortex circulation. Both are macroscopic fingerprints of non-radiative stationary states.

Diamagnetism and Paramagnetism

• Diamagnetism (e.g., noble gases, benzene rings): External magnetic fields perturb eigenmodes, inducing reverse circulations (Larmor precession or Landau orbitals), embodying a quantum version of Lenz's law;

• Paramagnetism/ferromagnetism: Local spins or orbital circulations align cooperatively under external fields, forming macroscopic magnetization. Their microscopic origin can be unified as "ordered arrangement of rotation–flux structures."

Mesoscopic and Molecular Circulations

• Ring currents in aromatic molecules (e.g., benzene) affect NMR chemical shifts;

• Persistent currents corresponding to Aharonov–Bohm oscillations have been observed in mesoscopic metal rings at millikelvin temperatures;

• Supercurrents in superconducting rings can persist for years without decay.

These phenomena collectively show that as long as the system is small enough, cold enough, and coherent enough, steady currents are a natural result.

V. "Are Elementary Particles Superconductors"? — Conceptual Discrimination and Accurate Expression

Although the analogy is intuitive, it is necessary to define it carefully:

Characteristics	Superconductors (macroscopic many-body)	Elementary particles/microscopically confined states
Origin	Spontaneous breaking of U(1) gauge symmetry	Single-particle/few-body quantum confinement
Flux quantum	Φ₀ = h/2e (Cooper pairs)	Φ = h/e (single electron)
Meissner effect	Macroscopic magnetic field repulsion	Only diamagnetic response
Zero-resistance transport	Can carry external currents	Only support intrinsic circulations

Therefore, a more accurate expression is:Elementary particles or microscopically confined states can support "non-dissipative steady-state circulations."They are like "microscopic non-dissipative loops" but not equivalent to superconductors.

The true unified picture is scale extension:

• Microscopic: Steady-state circulations → magnetic moments, diamagnetic/paramagnetic responses;

• Mesoscopic: Coherent rings → persistent currents, AB oscillations;

• Macroscopic: Coherent extension + energy gap protection → superconductivity, superfluidity, flux quantization, Meissner effect.

VI. Mechanistic Language from the NQT Perspective

Natural Quantum Theory (NQT) provides a consistent physical interpretation framework for this:

• Confined spectrum: Boundaries, potential wells, or geometry "close" the continuous spectrum into discrete frequency-locking points;

• Coherent frequency locking: Occupying eigenmodes enters a non-radiative steady state, forming perpetual currents;

• Topological protection: Phase winding numbers and single-valuedness provide "integer barriers" for circulations;

• Geometric reversibility: Changing cavity size, medium, or external fields causes the eigen spectrum to shift reversibly, with corresponding switches in circulation intensity and direction.

This not only explains stability but also provides controllability—completely consistent with experimental observations.

VII. Clarification on Compatibility with Traditional Narratives

"Accelerated charges must radiate" does not apply to quantum stationary states: stationary states are globally coherent solutions, and radiation fields cancel out in the far zone, consistent with atomic stability and discrete spectral lines;Ferromagnetism does not require "mysterious spins": it can be understood as the ordered alignment of local rotation–flux structures under exchange interactions, compatible with standard spin models but endowing them with geometric reality.

VIII. Three Testable Empirical Criteria (NQT-style)

1. Boundary-removal limit criterion: Removing constraints (e.g., increasing ring size, raising temperature) should cause circulation decay; reversible curves should be observed in controllable cavities/rings;

2. Geometric modulation criterion: Changing ring geometry or medium should induce reversible shifts in circulation and energy level splitting, consistent with "natural frequency locking" predictions;

3. Low-Q² form factor detection: In Compton or electron scattering with ultra-low momentum transfer, retrieve the minimal energy scale dependence related to "phase domain geometry" without violating the charge radius upper limit.

Conclusion: Unification from Microscopic Circulations to Macroscopic Quantum Phenomena

Macroscopic currents are easily dissipative because they are open, decoherent, and unprotected;Microscopic currents can be perpetual because they are confined, coherent, and topologically locked.

The "current maintenance" in electrons, diamagnetic/ferromagnetic atoms is a direct manifestation of non-radiative steady-state circulations.Amplifying these microscopic steady currents to the material scale through coherent extension and energy gap protection naturally gives rise to macroscopic quantum phenomena such as superconductivity, permanent magnetism, and topological electromagnetic responses.

Therefore, there is no need to call elementary particles "superconductors"—

They are the most basic "natural frequency-locking loops" in the universe.Their currents do not vanish simply because they have long resonated with spacetime and formed a self-consistent closed loop.

This also suggests that perpetual currents may be very important in the structure of elementary particles.