In SO(d)- and O(d)-invariant sectors of the U(N) d-matrix harmonic oscillator, microcanonical heat capacity is negative at low energy and turns positive at kcrit ~ N^2/4, producing a caloric fold analogous to AdS black holes.
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abstract
We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of $d$, $N\times N$ matrices invariant under the adjoint action of the symmetric group $S_N$. The approach is general to any discrete group. For a system of harmonic oscillators, i.e. for the non-interacting case, the partition function is given by the Molien-Weyl formula times the zero-point energy contribution. We further generalise the result to a system of non-square and complex matrices transforming under arbitrary representations of the gauge group.
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representative citing papers
The very-low-temperature bosonic singlet spectrum in BFSS_{d+1} is controlled by d(d+1)/2 quadratic Gram operators Tr(X_a X_b), with an exact BFSS_3 = (BFSS_2)^3 factorization at (d,N)=(2,2).
Gram/Wishart/Stiefel reformulation of N=2 large-d BFSS/BMN endpoints absorbs -A into a shifted mass and recovers the universal continuum -2d DΛ-channel after non-polynomial transverse completion.
Establishes equivalence between endpoint and Molien-Weyl formulations for large-d BFSS models on the lattice and derives finite continuum D-channel via a toy holonomy potential model.
Position paper claiming that distributed training across massive edge devices can overcome data depletion and centralized compute monopolies in LLM scaling.
citing papers explorer
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Negative heat capacities in spherically symmetric sectors of $d$-matrix quantum mechanics
In SO(d)- and O(d)-invariant sectors of the U(N) d-matrix harmonic oscillator, microcanonical heat capacity is negative at low energy and turns positive at kcrit ~ N^2/4, producing a caloric fold analogous to AdS black holes.
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Molien--Weyl Singlet Counting and BFSS$_2$--Factorization in Gaussian Matrix QM
The very-low-temperature bosonic singlet spectrum in BFSS_{d+1} is controlled by d(d+1)/2 quadratic Gram operators Tr(X_a X_b), with an exact BFSS_3 = (BFSS_2)^3 factorization at (d,N)=(2,2).
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Gram--Wishart--Stiefel formulation of the $N=2$, large--$d$ gauge theory in 1D
Gram/Wishart/Stiefel reformulation of N=2 large-d BFSS/BMN endpoints absorbs -A into a shifted mass and recovers the universal continuum -2d DΛ-channel after non-polynomial transverse completion.
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Endpoint formulation and Molien--Weyl structure for the \(N=2\), large--\(d\) BFSS/BMN models
Establishes equivalence between endpoint and Molien-Weyl formulations for large-d BFSS models on the lattice and derives finite continuum D-channel via a toy holonomy potential model.
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Will LLMs Scaling Hit the Wall? Breaking Barriers via Distributed Resources on Massive Edge Devices
Position paper claiming that distributed training across massive edge devices can overcome data depletion and centralized compute monopolies in LLM scaling.
- A Double--Scaling Large--\(d\) Saddle of BFSS/BMN Matrix Quantum Mechanics