Statistical Mechanics for Non-Hermitian Quantum Systems

We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in conjunction with the system's Hamiltonian, dictates the equilibrium state. By elucidating the relationship between the Hamiltonian and the supported conserved quantity, we propose criteria for discerning equilibrium states with finite relaxation times. Although our findings indicate that only non-Hermitian systems with real energy spectrum precisely possess such conserved quantities, we also demonstrate that an effective conserved quantity can manifest in certain systems with complex energy spectra. The effective conserved quantity, alongside the effective transitions within their associated subspace, collectively determines the system's equilibrium state. Our results provide valuable insights into non-Hermitian systems across various contexts and hold potential for applications in a diverse range of physical systems

Towards Real-World Test-Time Adaptation: Tri-Net Self-Training with Balanced Normalization

Test-Time Adaptation aims to adapt source domain model to testing data at inference stage with success demonstrated in adapting to unseen corruptions. However, these attempts may fail under more challenging real-world scenarios. Existing works mainly consider real-world test-time adaptation under non-i.i.d. data stream and continual domain shift. In this work, we first complement the existing real-world TTA protocol with a globally class imbalanced testing set. We demonstrate that combining all settings together poses new challenges to existing methods. We argue the failure of state-of-the-art methods is first caused by indiscriminately adapting normalization layers to imbalanced testing data. To remedy this shortcoming, we propose a balanced batchnorm layer to swap out the regular batchnorm at inference stage. The new batchnorm layer is capable of adapting without biasing towards majority classes. We are further inspired by the success of self-training~(ST) in learning from unlabeled data and adapt ST for test-time adaptation. However, ST alone is prone to over adaption which is responsible for the poor performance under continual domain shift. Hence, we propose to improve self-training under continual domain shift by regularizing model updates with an anchored loss. The final TTA model, termed as TRIBE, is built upon a tri-net architecture with balanced batchnorm layers. We evaluate TRIBE on four datasets representing real-world TTA settings. TRIBE consistently achieves the state-of-the-art performance across multiple evaluation protocols. The code is available at \url{https://github.com/Gorilla-Lab-SCUT/TRIBE}.Comment: 23 pages, 7 figures and 22 table

Non-Hermitian Maxwell's Demon

Maxwell's demon was first introduced by Maxwell in 1871 to discuss the limitations of the second law of thermodynamics due to addition information flow. In this paper, an alternative type of Maxwell's demon -- non-Hermitian Maxwell's demon is uncovered that shows quite different properties as the original Maxwell's demon and leads to rich physics phenomena in non-Hermitian systems, such as mismatch between single-body and many-body properties, Bose-Einstein condensation at arbitrary high temperature, phase transition that violates the Goldstone theorem. This provides an alternative degree of freedom to tune quantum many-body systems and realize exotic quantum phases and phase transitions

Symmetry classes of dissipative topological insulators with edge dark state

We classify the dissipative topological insulators (TIs) with edge dark states (EDS) by using the 38-fold way of non-Hermitian systems in this paper. The dissipative dynamics of these quadratic open fermionic systems is captured by a non-Hermitian single-particle matrix which contains both the internal dynamics and the dissipation, refereed to as damping matrix $X$. And the dark states in these systems are the eigenmodes of $X$ which the eigenvalues' imaginary part vanishes. However, there is a constraint on $X$, namely that the modes in which the eigenvalues' imaginary parts are positive are forbidden. In other words, the imaginary line-gap of $X$ is ill-defined, so the topological band theory classifying the dark states can not be applied to $X$. To reveal the topological protection of EDS, we propose the double damping matrix $\tilde{X} = \text{diag}\left( X, X^* \right)$, where the imaginary line-gap is well defined. Thus, the 38-fold way can be applied to $\tilde{X}$, and the topological protection of the EDS is uncovered. Different from previous studies of EDS in purely dissipative dynamics, the EDS in the dissipative TIs are robust against the inclusion of Hamiltonians. Furthermore, the topological classification of $\tilde{X}$ not only reflects the topological protection of EDS in dissipative TIs but also provides a paradigm to predict the appearance of EDS in other open free fermionic systems.Comment: 8 pages, 4 figure

Efficacy of the Combination of Voriconazole and Caspofungin in Experimental Pulmonary Aspergillosis by Different Aspergillus Species

OBJECTIVES: Invasive pulmonary aspergillosis (IPA) caused by Aspergillus fumigatus, Aspergillus flavus, or Aspergillus niger is associated with high mortality. We evaluated the efficacy and compared the therapeutic effect differences of voriconazole (VRC) in combination with caspofungin (CAS) in transiently neutropenic rats infected by A. fumigatus, A. flavus, or A. niger. METHODS: Treatment groups consisted of VRC (10 mg/kg q12 h) monotherapy, CAS (1 mg/kg/day) monotherapy, combination of VRC (10 mg/kg q12 h) + CAS (1 mg/kg/day), and no drug for 10 consecutive days. The efficacy and the difference in the treatments were evaluated through prolongation of survival, reduction in serum galactomannan levels and residual fungal burden, and histological studies. RESULTS: For all the strains, the combination of VRC and CAS led to significant prolongation in survival (P < 0.05) and reduction in residual fungal burden (P < 0.05) compared with CAS alone, and decrease in serum galactomannan levels (P < 0.05) compared with either agent alone. The survival in the combined therapy groups was significantly improved compared to VRC monotherapy for the strains of A. flavus and A. niger (P < 0.05), but no significant difference for the strains of A. fumigatus (P > 0.05). CONCLUSIONS: Combination of VRC and CAS was synergistic in IPA by A. flavus and A. niger, but small efficacy benefits in IPA by A. fumigatus

1,3-Bis[(4-methylbenzylidene)amino­oxy]propane

The title bis­oxime compound, C19H22N2O2, synthesized by the reaction of 4-methyl-2-hydroxy­benzaldehyde with 1,3-bis­(amino­oxy)propane in ethanol, adopts a V-shaped conformation. The dihedral angle between the rings is 84.59 (3)°. The mol­ecule is disposed about a crystallographic twofold rotation axis, with one C atom lying on the axis. In the crystal, mol­ecules are packed by C—H⋯π(Ph) inter­actions, forming chains