MATLAB QVC-TEVC Tunneling Simulation Suite

Quasiparticle Tunneling, Schwinger Pair Production & Hopfion Nucleation

This MATLAB simulation suite models the full chain of quantum vacuum catalyzation effects in a Twisted Engineered Vacuum Crystal (TEVC) — a van der Waals heterostructure where the moire superlattice creates a tunable analog quantum vacuum.

The simulation covers:

Moire superlattice potential from twisted TMD bilayer (MoSe₂/WSe₂)
Catalyzon quasiparticle — the emergent vacuum-matter hybrid excitation with dispersion omega_cat(k, A_ZPF)
Transfer-matrix tunneling through periodic moire barriers, with ZPF-enhanced barrier reduction
Schwinger-analog pair production where the effective critical field drops ~14 orders of magnitude below the QED threshold
Hopfion topological solitons — nucleation energetics and BEC-hopfion phase diagram
Twist angle dependence with magic-angle flat-band enhancement
Rashba spin-orbit coupling and chiral Berry curvature transport

Material System

The default parameters target a TMD heterobilayer (MoSe₂/WSe₂ or similar) with:

| Parameter | Value | Description | |-----------|-------|-------------| | a | 0.328 nm | Lattice constant | | m* | 0.45 m_e | Exciton effective mass | | epsilon | 4.5 | Dielectric constant | | J | 15 meV | Interlayer tunneling | | V₀ | 25 meV | Moire potential amplitude | | theta | 1.1 deg | Twist angle (near magic angle) |

Download Simulation SuiteRequires MATLAB R2020a+ (no additional toolboxes needed). Place all files in one directory and run QVC_TEVC_Main.
QVC_TEVC_Main.mMaster driver script — runs everything, generates 8 figures~36 KBcompute_moire_potential.mMoire superlattice V(r) from twisted bilayer G-vectors~2 KBcatalyzon_dispersion.mCatalyzon ω_cat(k, A_ZPF) from 3-mode hybridization~4 KBtransfer_matrix_1d.mTransfer matrix T(E) through periodic moire barriers~3 KBschwinger_rate.mSchwinger-analog pair production with reduced E_cr~3 KBhopfion_nucleation.mHopfion energetics, nucleation rates, BEC-hopfion phase diagram~5 KBzpf_vacuum_catalyzation.mUnified ZPF effects: gap, tunneling, Schwinger, entropy~4 KB

How to Run

Download all 7 .m files above into a single directory
Open MATLAB (R2020a or later, no additional toolboxes required)
Navigate to the directory: cd path/to/QVC_TEVC_Simulation
Run: QVC_TEVC_Main
All 8 figures generate sequentially (~30 seconds total)

Adjusting Parameters

All physical parameters are defined in Section 1 of QVC_TEVC_Main.m. Key parameters to explore:

tevc.theta_deg — twist angle (try 0.5 to 3.5 degrees)
tevc.J — interlayer tunneling energy (5 to 50 meV)
qvc.A_ZPF_range — ZPF amplitude sweep range
topo.QH — Hopf charge (integer)
topo.alpha_R — Rashba SOC strength

Dark Theme

All figures render with dark backgrounds and colored traces matching the website's sci-fi aesthetic. Set set(gcf, 'InvertHardcopy', 'off') is already included to preserve dark backgrounds when saving/printing.

Physics Summary

The central insight of this simulation is the mapping between QED vacuum pair production and condensed matter quasiparticle phenomena:

| QED Vacuum | TEVC Analog | |------------|-------------| | Electron mass m_e | Exciton effective mass m* | | 2m_e c² gap | Excitonic gap Delta_cat | | Compton wavelength | Coherence length xi | | E_cr = 1.3 x 10^18 V/m | E_cr^eff ~ 10^4 V/m | | Virtual e+e- pairs | Virtual exciton-hole pairs | | Dirac vacuum | Excitonic BEC condensate |

The vacuum catalyzation parameter A_ZPF tunes the system from a stable gapped insulator (A = 0) through the catalyzon regime to the quantum critical point (A ~ 0.5) where the gap collapses, the Schwinger threshold vanishes, and pair production becomes copious.

Mineral Björn Hoiland