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At least 55 records · Page 3

Coherence-Induced Deep Thermalization Transition in Random Permutation Quantum Dynamics

We report a phase transition in the projected ensemble—the collection of postmeasurement wave functions of a local subsystem obtained by measuring its complement. The transition emerges in systems undergoing random permutation dynamics, a type of quantum time evolution wherein computational basis states are shuffled without creating superpositions. It separates a phase exhibiting deep thermalization, where the projected ensemble is distributed over Hilbert space in a maximally entropic fashion (Haar random), from a phase where it is minimally entropic (“classical bit-string ensemble”). Crucially, this deep thermalization transition is invisible to the subsystem’s density matrix, which always exhibits thermalization to infinite temperature across the phase diagram. Through a combination of analytical arguments and numerical simulations, we show that the transition is tuned by the total amount of injected by the input state and the measurement basis, and is exhibited robustly across different microscopic models. Our findings represent a novel form of ergodicity-breaking universality in quantum many-body dynamics, characterized not by a failure of regular thermalization, but rather by a failure of deep thermalization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Scattering neutrinos, spin models, and permutations

We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with N degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to N , nontrivial eigenvalues, in distinction to the classic Heisenberg spin-glass models, leading to distinct behavior in both the high-temperature and low-temperature regimes. When the momenta of the neutrinos are uniform and random in directions, we can calculate the large- N partition function for the quantum Heisenberg model. In particular, the high-temperature partition function predicts a non-Gaussian density of states, providing interesting counterexamples showing the limits of general theorems on the density of states for quantum spin models. We can repeat the same argument for classical Heisenberg models, also known as rotor models, and we find the high-temperature expansion is completely controlled by the eigenvalues of the coupling matrix, and again predicts non-Gaussian behavior for the density of states as long as the number of eigenvalues does not scale linearly with N . Indeed, we derive the amusing fact that these partition functions are essentially the generating function for counting permutations in the high-temperature regime. Finally, for the case relevant to neutrinos in a supernova, we identify the low-temperature phase as a unique state with the direction of the momenta of the neutrino dictating its coherent state in flavor-space, a state we dub the “flavor-momentum-locked” state. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Adaptive QM/MM for Molecular Dynamics Simulations: 5. On the Energy-Conserved Permuted Adaptive-Partitioning Schemes

In combined quantum-mechanical/molecular-mechanical (QM/MM) dynamics simulations, the adaptive-partitioning (AP) schemes reclassify atoms on-the-fly as QM or MM in a smooth manner. This yields a mobile QM subsystem with contents that are continuously updated as needed. Here, we tailor the Hamiltonian adaptive many-body correction (HAMBC) proposed by Boreboom et al. [J. Chem. Theory Comput. 2016, 12, 3441] to the permuted AP (PAP) scheme. The treatments lead to the HAMBC-PAP method (HPAP), which both conserves energy and produces accurate solvation structures in the test of “water-in-water” model system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Densely Connected G-invariant Deep Neural Networks with Signed Permutation Representations

We introduce and investigate, for finite groups G, G-invariant deep neural network (GDNN) architectures with ReLU activation that are densely connected- i.e., include all possible skip connections. In contrast to other G-invariant architectures in the literature, the preactivations of theG-DNNs presented here are able to transform by signed permutation representations (signed perm-reps) of G. Moreover, the individual layers of the G-DNNs are not required to be G-equivariant; instead, the preactivations are constrained to be G-equivariant functions of the network input in a way that couples weights across all layers. The result is a richer family of G-invariant architectures never seen previously. We derive an efficient implementation of G-DNNs after a reparameterization of weights, as well as necessary and sufficient conditions for an architecture to be "admissible"- i.e., nondegenerate and inequivalent to smaller architectures. We include code that allows a user to build a G-DNN interactively layer-by-layer, with the final architecture guaranteed to be admissible. We show that there are far more admissible G-DNN architectures than those accessible with the "concatenated ReLU" activation function from the literature. Finally, we apply G-DNNs to two example problems--(1) multiplication in --1, 1} (with theoretical guarantees) and (2) 3D object classification--finding that the inclusion of signed perm-reps significantly boosts predictive performance compared to baselines with only ordinary (i.e., unsigned) perm-reps.

97 MATHEMATICS AND COMPUTING↗

Enhanced Integer Permutation based Genetic Algorithm for Optimization of Tube-Fin Heat Exchanger Circuitry with Splits and Merges

Tube-fin heat exchangers (HXs) are widely used in air-conditioning and heat pump applications. The performance of these heat exchangers is strongly influenced by the refrigerant circuitry. Studies have proved that by optimizing the refrigerant circuitry, the performance of HXs can be significantly improved. In our previous research, an Integer Permutation based Genetic Algorithm (IPGA) was developed to obtain the optimal circuitry designs. Our previous research showed that IPGA demonstrates superior capability to obtain better refrigerant circuitries with lower computational cost than the other methods in literature. And the optimal circuitry designs obtained from IPGA are manufacturable with the available tooling. However, the IPGA developed previously cannot generate designs with splitting and merging of circuits. To remedy this limitation, a new chromosome which can represent circuitry with splitting and merging of circuits is developed. In addition to the six genetic operators implemented previously, two new genetic operators are developed to generate splits and merges. As a result, the enhanced IPGA can explore the solution space more thoroughly than the previous IPGA. A case study using an evaporator from an A-type indoor unit shows that, given the similar capacity improvements obtained from the enhanced IPGA compared with the previous IPGA, the refrigerant pressure drop reduction obtained from the enhanced IPGA is 26.5% compared against 1.0% pressure drop reduction from the previous IPGA. The benchmark of the enhanced IPGA with other methods in literature demonstrates that the enhanced IPGA can generate circuitry designs with performance superior to those obtained from other methods.

LI, Zhenning↗

Late Breaking Results: COPPER: Computation Obfuscation by Producing Permutations for Encoding Randomly

Deployed embedded devices face security risks due to increased ease of physical access to the devices by unauthorized users. Capable adversaries can intercept a device to recover the data in memory, including results of performed sensitive computations. Device owners require data confidentiality on their physically insecure devices. To satisfy this goal we implement a novel method, COPPER (Computation Obfuscation by Producing Permutations for Encoding Randomly), to create data which never exists on the device digitally in plaintext format and which is subsequently used for computation. In this paper we utilize COPPER to calculate a moving average computation on encoded data.

embedded systems↗

Structure and properties of the algebra of partially transposed permutation operators

We consider the structure of algebra of operators, acting in n-fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its regular representation, we derive basic properties of the algebra. In particular, we describe all irreducible representations of the algebra of partially transposed operators and derive expressions for matrix elements of the representations. It appears that there are two kinds of irreducible representations of the algebra. The first one is strictly connected with the representations of the group S(n − 1) induced by irreducible representations of the group S(n − 2). The second kind is structurally connected with irreducible representations of the group S(n − 1)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗