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Topological band theory has been studied for free fermions for decades, and one of the most profound physical results is the bulk-boundary correspondence. Recently a trend in topological physics is extending topological classification to mixed state. Here, we focus on Gaussian mixed states where the modular Hamiltonians of the density matrix are quadratic free fermion models and can be classified by topological invariants. The bulk-boundary correspondence is then manifested as stable gapless modes of the modular Hamiltonian and degenerate spectrum of the density matrix. In this letter, we show that these gapless modes can be detected by the full counting statistics, mathematically described by a function introduced as F({\theta}). We show that a divergent derivative at {\theta} = {\pi} probes the gapless modes in the modular Hamiltonian. We can introduce a topological indicator whose quantization to unity senses topologically nontrivial mixed states. We present the physical intuition of these results and also demonstrate these results with concrete models in both one- and two-dimensions. Our results pave the way for revealing the physical significance of topology in mixed states., Comment: 7pages, 3figures

Non-Hermitian skin effect (NHSE), namely that eigenstates of non-Hermitian Hamiltonains are localized at one boundary in the open boundary condition, attracts great interest recently.In this paper, we investigate the skin effect in one-dimensional dissipative quantum many-body systems, which we call the Liouvillian skin effect (LSE). We rigorously identify the existence of LSE for generalized boundary conditions by solving the Liouvillian superoperator of an exactly solvable model with the advantage of Bethe ansatz. The LSE is sensitive to boundary conditions where the signature is reflected in eigenfunctions of the system. We confirm that the LSE is fragile to a tiny co-flow boundary hopping with non-Hermitian current but can survive for a counter-flow boundary hopping in the thermodynamic limit. Our work provides a prototypical example of exactly solvable dissipative quantum many-body lattice systems exhibiting LSE for generalized boundary conditions. It can be further extended to other integrable open quantum many-body models., Comment: 15 pages, 5 figures. Comments are welcome

The presence of tertiary lymphoid structures (TLSs) on pancreatic pathological images is an important prognostic indicator of pancreatic tumors. Therefore, TLSs detection on pancreatic pathological images plays a crucial role in diagnosis and treatment for patients with pancreatic tumors. However, fully supervised detection algorithms based on deep learning usually require a large number of manual annotations, which is time-consuming and labor-intensive. In this paper, we aim to detect the TLSs in a manner of few-shot learning by proposing a weakly supervised segmentation network. We firstly obtain the lymphocyte density maps by combining a pretrained model for nuclei segmentation and a domain adversarial network for lymphocyte nuclei recognition. Then, we establish a cross-scale attention guidance mechanism by jointly learning the coarse-scale features from the original histopathology images and fine-scale features from our designed lymphocyte density attention. A noise-sensitive constraint is introduced by an embedding signed distance function loss in the training procedure to reduce tiny prediction errors. Experimental results on two collected datasets demonstrate that our proposed method significantly outperforms the state-of-the-art segmentation-based algorithms in terms of TLSs detection accuracy. Additionally, we apply our method to study the congruent relationship between the density of TLSs and peripancreatic vascular invasion and obtain some clinically statistical results.

Peripancreatic vessel segmentation and anatomical labeling play extremely important roles to assist the early diagnosis, surgery planning and prognosis for patients with pancreatic tumors. However, most current techniques cannot achieve satisfactory segmentation performance for peripancreatic veins and usually make predictions with poor integrity and connectivity. Besides, unsupervised labeling algorithms cannot deal with complex anatomical variation while fully supervised methods require a large number of voxel-wise annotations for training, which is very labor-intensive and time-consuming. To address these problems, we propose our Automated Peripancreatic vEssel Segmentation and lAbeling (APESA) framework, to not only highly improve the segmentation performance for peripancreatic veins, but also efficiently identify the peripancreatic artery branches. There are two core modules in our proposed APESA framework: iterative trunk growth module (ITGM) for vein segmentation and weakly supervised labeling mechanism (WSLM) for artery branch identification. Our proposed ITGM is composed of a series of trunk growth modules, each of which chooses the most reliable trunk of a basic vessel prediction by the largest connected constraint, and seeks for the possible growth branches by branch proposal network. Our designed iterative process guides the raw trunk to be more complete and fully connected. Our proposed WSLM consists of an unsupervised rule-based preprocessing for generating pseudo branch annotations, and an anatomical labeling network to learn the branch distribution voxel by voxel. We achieve Dice of 94.01% for vein segmentation on our collected dataset, which boosts the accuracy by nearly 10% compared with the state-of-the-art methods. Additionally, we also achieve Dice of 97.01% on segmentation and competitive performance on anatomical labeling for peripancreatic arteries.

Pancreatic duct dilation indicates a high risk of various pancreatic diseases. Segmentation of dilated pancreatic ducts on computed tomography (CT) images shows the potential to assist the early diagnosis, surgical planning and prognosis. Because of the ducts' tiny sizes, slender tubular structures and the surrounding distractions, most current researches on pancreatic duct segmentation achieve low accuracy and always have segmentation errors on the terminal parts of the ducts. To address these problems, we propose a terminal guidance mechanism called cascaded terminal guidance network (CTG-Net). Firstly, a terminal attention mechanism is established on the skeletons extracted from the coarse predictions. Then, to get fine terminal segmentation, a subnetwork is designed for jointly learning the local intensity from the original images, feature cues from coarse predictions and global anatomy information from the pancreas distance transform maps. Finally, a terminal distraction attention module which explicitly learns the distribution of the terminal distraction is proposed to reduce the false positive and false negative predictions. We also propose a new metric called tDice to measure the terminal segmentation accuracy for targets with tubular structures and two segmentation metrics for distractions. We collect our dilated pancreatic duct segmentation dataset with 150 CT scans from patients with 5 types of pancreatic tumors. Experimental results on our dataset show that our proposed approach boosts dilated pancreatic duct segmentation accuracy by nearly 20% compared with the existing results, and achieves more than 9% improvement for the terminal segmentation accuracy compared with the state-of-the-art methods.

The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian. Since the topological classification of such Hamiltonians depends on their symmetry classes, a primary issue we address is determining the requirement for the Lindbladian operators, under which the modular Hamiltonian can preserve its symmetry class during the dynamical evolution. We solve this problem for the fermionic Gaussian state and for the modular Hamiltonian being a quadratic operator of a set of fermionic operators. When these conditions are satisfied, along with a nontrivial topological classification of the symmetry class of the modular Hamiltonian, a topological transition can occur as time evolves. We present two examples of dissipation-driven topological transitions where the modular Hamiltonian lies in the AIII class with U(1) symmetry and the DIII class without U(1) symmetry. By a finite size scaling, we show that this density matrix topology transition occurs at a finite time. We also present the physical signature of this transition., Comment: 8 pages, 2 figure

Non-Hermitian skin effect (NHSE) is a unique feature studied extensively in non-interacting non-Hermitian systems. In this work, we extend the NHSE originally discovered in non-interacting systems to interacting many-body systems by investigating an exactly solvable non-Hermitian model, i.e., the prototypical Lieb-Liniger Bose gas with imaginary vector potential. We show that this non-Hermitian many-body model can also be exactly solved through Bethe ansatz. By solving the Bethe ansatz equations accurately, the explicit eigenfunction is obtained, and the model's density profiles and momentum distributions are calculated to characterize the NHSE quantitatively. We find that the NHSE is gradually suppressed on the repulsive side but does not vanish as the repulsive interaction strength increases. On the attractive side, the NSHE for bound-state solutions is enhanced as interaction strength grows. In contrast, for the scattering state the NHSE shows a non-monotonic behavior in the attractive side. Our work provides the first example of the NHSE in exactly solvable many-body systems, and we envision that it can be extended to other non-Hermitian many-body systems, especially to integrable models., Comment: 8 pages, 4 figures. Comments and missing references are welcome

Non-Hermitian skin effect, namely that the eigenvalues and eigenstates of a non-Hermitian tight-binding Hamiltonian have significant differences under open or periodic boundary conditions, is a remarkable phenomenon of non-Hermitian systems. Inspired by the presence of the non-Hermitian skin effect, we study the evolution of wave-packets in non-Hermitian systems, which can be determined using the single-particle Green's function. Surprisingly, we find that in the thermodynamical limit, the Green's function does not depend on boundary conditions, despite the presence of skin effect. We proffer a general proof for this statement in arbitrary dimension with finite hopping range, with an explicit illustration in the non-Hermitian Su-Schrieffer-Heeger model. We also explore its applications in non-interacting open quantum systems described by the master equation, where we demonstrate that the evolution of the density matrix is independent of the boundary condition., Comment: 5 pages, 3 figures

In this letter we point out that the Lindblad spectrum of a quantum many-body system displays a segment structure and exhibits two different energy scales in the strong dissipation regime. One energy scale determines the separation between different segments, being proportional to the dissipation strength, and the other energy scale determines the broadening of each segment, being inversely proportional to the dissipation strength. Ultilizing a relation between the dynamics of the second R\'enyi entropy and the Lindblad spectrum, we show that these two energy scales respectively determine the short- and the long-time dynamics of the second R\'enyi entropy starting from a generic initial state. This gives rise to opposite behaviors, that is, as the dissipation strength increases, the short-time dynamics becomes faster and the long-time dynamics becomes slower. We also interpret the quantum Zeno effect as specific initial states that only occupy the Lindblad spectrum around zero, for which only the broadening energy scale of the Lindblad spectrum matters and gives rise to suppressed dynamics with stronger dissipation. We illustrate our theory with two concrete models that can be experimentally verified., Comment: 5 pages, 4 figures

We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit for quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a by product, the algorithm also gives access to low energy excitation states. We demonstrate applications to thermal properties and excitation spectra of the quantum Ising model with resources that are feasible on near-term quantum computers., Comment: 7 pages, 5 figures, code: https://github.com/wangleiphy/BetaVQE.jl