Krestianstvo Abstract Holographic Computer: Bose–Einstein condensates and Fermionic superfluids.

The Krestianstvo Abstract Holographic Computer (AHC) medium can now hold the quantum condensate dynamics in the field. Bose–Einstein condensates (BECs) are native c-fields. Fermionic superfluids use Bogoliubov–de Gennes (BdG) pairing on the medium’s own dispersion and matrix-free.

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Core Principles: Field Medium Over Matrices

Traditional quantum simulations rely on large Hamiltonian matrices, Fock-space occupation numbers, and single-particle orbital expansions. In contrast, the Krestianstvo Abstract Holographic Computer medium treats a condensate as a macroscopic continuum wavefunction living on a closed periodic grid (torus).

Each slot owns a contiguous complex field representing a coherent quantum state or condensate reservoir. Time evolution and propagation are executed natively via the medium's exact Fourier–Mukai transforms and dispersion operators, incorporating saturable nonlinearities (Kerr focusing with saturation) rather than pairwise matrix interactions.

Native Bose-Einstein Condensates & Replicating Andrews et al. (1997)

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The landmark 1997 experiment by M. R. Andrews et al. (published in Science) demonstrated matter-wave interference by releasing two independent Bose–Einstein condensates from a double-well trap and observing interference fringes as they overlapped.
The Krestianstvo Abstract Holographic Computer medium reproduces this phenomenon natively.

The field is the stochastic Gross–Pitaevskii c-field. The medium’s own law, plus a bath (noise, damping, temperature), drives it. A native well is the trap, the slot’s Kerr is the repulsion, and the cap sets the atom number. Cooling it shows condensation and vortices annihilating, and a quench shows Kibble–Zurek vortices.

Two independent condensates form apart in a written double well within the same slot. Their relative phase is not set by hand. It comes from the bath’s noise seed, so a new seed gives a new phase.

When the well is removed, the two wavepackets expand and overlap. The medium propagates the field by its Fresnel operator and the bath gives the noise and damping. The overlapping packets interfere, and the density shows fringes at a phase nobody set.
This occurs without tracking individual bosons or building Fock states. Phase coherence and interference emerge from the wave equation of the medium.

Wigner–Weyl Phase Space: Watching Condensation as it Happens

The Krestianstvo Abstract Holographic Computer medium can show a condensing field in phase space, and also as a time series. Both views are built from the field the medium already holds, so they need no extra matrices.

The condensate in phase space (x, k). The viewer shows the Wigner function of the condensate’s, averaged over the read beats the way the time-of-flight image is. In the cooling act, a hot cloud appears as a broad thermal halo. As the field condenses, a compact blob grows out of it, which is the Penrose–Onsager rise, seen directly in phase space. Negative regions of (shown in blue) mark interference. In the Andrews sequence, the two condensates leave a cross term between them that oscillates, so their relative phase can be read in phase space.

Time series (Wigner–Ville). The viewer also computes a Wigner–Ville distribution of a complex signal taken beat by beat. The signal can be the field at a probe cell, a 5×5 average about it, or the whole field’s mode (whose growth marks condensation). For the two wells, it is the relative phasor. A steady winding shows as a flat line, a Josephson swing as an oscillation, and a chirp as a slope, with the first moment drawn as the instantaneous Josephson frequency.

Fermionic Condensates & Pairing

Because Pauli exclusion cannot live in a single c-field, the fermionic part is a ladder of BdG solvers over the medium’s own dispersion. The matrix-free native field relaxes to equilibrium.

Phenomena shown: the ideal Fermi sea, the paired state, the BEC–BCS crossover, the critical temperature, and a vortex with its core states, the Cooper problem and a two-fermion bound pair.

Replicated computation

Two web browsers are running deterministically the 1997 experiment by M. R. Andrews of interference between two independent Bose-Einstein condensates (BECs). That is the Krestianstvo holographic computer medium in it's full action, demonstrating replicated computation in continuous time on network between peers.

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