Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspect...Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning architecture that can automatically develop the concept of the quantum wave function and discover the Schr?dinger equation from simulated experimental data of the potential-todensity mappings of a quantum particle. This introspective learning architecture contains a machine translator to perform the potential to density mapping, and a knowledge distiller auto-encoder to extract the essential information and its update law from the hidden states of the translator, which turns out to be the quantum wave function and the Schr?dinger equation. We envision that our introspective learning architecture can enable machine learning to discover new physics in the future.展开更多
In this paper we first compute the out-of-time-order correlators(OTOC) for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a...In this paper we first compute the out-of-time-order correlators(OTOC) for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase,while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second Rényi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.展开更多
In this work, we apply a principal component analysis （PCA） method with a kernel trick to study the classification of phases and phase transitions in classical XY models of frustrated lattices. Compared to our previ...In this work, we apply a principal component analysis （PCA） method with a kernel trick to study the classification of phases and phase transitions in classical XY models of frustrated lattices. Compared to our previous work with the linear PCA method, the kernel PCA can capture nonlinear functions. In this case, the Z2 chiral order of the classical spins in these lattices is indeed a nonlinear function of the input spin configurations. In addition to the principal component revealed by the linear PCA, the kernel PCA can find two more principal components using the data generated by Monte Carlo simulation for various temperatures as the input. One of them is related to the strength of the U（1） order parameter, and the other directly manifests the chiral order parameter that characterizes the Z2 symmetry breaking. For a temperature-resolved study, the temperature dependence of the principal eigenvalue associated with the Z2 symmetry breaking clearly shows second-order phase transition behavior.展开更多
Recently an experiment on superradiant transition of a Bose condensate in two crossed beam cavities has been reported by Léonard et al. in Nature 543, 87(2017). The surprise is they find that across the superradi...Recently an experiment on superradiant transition of a Bose condensate in two crossed beam cavities has been reported by Léonard et al. in Nature 543, 87(2017). The surprise is they find that across the superradiant transition, the cavity light can be emitted in any superposition of these two cavity modes. This indicates an additional U(1) symmetry that does not exist in the full Hamiltonian. In this paper we show that this symmetry is an emergent symmetry in the vicinity of the phase transition. We identify all the necessary conditions that are required for this emergent U(1) symmetry and show that this experiment is a special case that satisfies these conditions. We further show that the superradiant transition in this system can also be driven to a first order one when the system is tuned away from the point having the emergent symmetry.展开更多
Spin-orbit coupling is a relativistic effect for the charge particles such as electrons.It has been found that the spin-orbit coupling plays an important role in many branches of physics,for instance,in condensed matt...Spin-orbit coupling is a relativistic effect for the charge particles such as electrons.It has been found that the spin-orbit coupling plays an important role in many branches of physics,for instance,in condensed matter physics,the spin-orbit cou-展开更多
In 1970,Vitaly Efimov found an interesting phenomenon in a quantum three-body problem,which is now known as the Efimov effect.Efimov found that when the two-body in teraction potential is short-ranged and is tuned to ...In 1970,Vitaly Efimov found an interesting phenomenon in a quantum three-body problem,which is now known as the Efimov effect.Efimov found that when the two-body in teraction potential is short-ranged and is tuned to the vicinity of an s-wave resonance,an inhnite number of three-body bound states emerge and their eigenenergies En form a geometric sequence as En=-|Eo|exp(—2m/So).展开更多
The Efimov effect is defined as a quantum state with discrete scaling symmetry and a universal scaling factor. It has attracted considerable interests from nuclear to atomic physics communities. In a Dirac semi-metal,...The Efimov effect is defined as a quantum state with discrete scaling symmetry and a universal scaling factor. It has attracted considerable interests from nuclear to atomic physics communities. In a Dirac semi-metal, when an electron interacts with a static impurity through a Coulombic interaction, the same kinetic scaling and the interaction energy results in the Efimov effect. However, even when the Fermi energy lies exactly at the Dirac point, the vacuum polarization of the electron-hole pair fluctuation can still screen the Coulombic interaction, which leads to deviations from the scaling symmetry and eventually breaks down of the Efimov effect. This energy distortion of the Efimov states due to vacuum polarization is a relativistic electron analogy of the Lamb shift for the hydrogen atom. Motivated by the recent experimental observations in two- and three-dimensional Dirac semi-metals, we herein investigate this many-body correction to the Efimov effect and the conditions that allow some of the Efimov-like quasi-bound states to be observed in these condensed matter experiments.展开更多
The cocktail party problem refers to the phenomenon that the brain of a listener can focus on a single voice while filtering out a range of other voices in a multi-talker situation,say,in a cocktail party[1].This sele...The cocktail party problem refers to the phenomenon that the brain of a listener can focus on a single voice while filtering out a range of other voices in a multi-talker situation,say,in a cocktail party[1].This selective attention problem was firstly defined as the"cocktail party problem"(CPP)by Cherry[2]in 1953.In recent years,machine-learning based approaches to solve the CPP were essential for many industrial applications such as automated speech recognition.The independent component analysis(ICA)is such an algorithm particularly suitable for the CPP.The CPP also has applications in physical science such as astrophysics data analysis[3,4].展开更多
基金financially supported by the National Key Research and Development Program of China (2016YFA0301600)the National Natural Science Foundation of China (11734010)the support of the China Scholarship Council
文摘Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning architecture that can automatically develop the concept of the quantum wave function and discover the Schr?dinger equation from simulated experimental data of the potential-todensity mappings of a quantum particle. This introspective learning architecture contains a machine translator to perform the potential to density mapping, and a knowledge distiller auto-encoder to extract the essential information and its update law from the hidden states of the translator, which turns out to be the quantum wave function and the Schr?dinger equation. We envision that our introspective learning architecture can enable machine learning to discover new physics in the future.
基金supported by the National Key Research and Development Plan (2016YFA0301600)the National Natural Science Foundation of China (11325418)Tsinghua University Initiative Scientific Research Program
文摘In this paper we first compute the out-of-time-order correlators(OTOC) for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase,while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second Rényi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.
文摘In this work, we apply a principal component analysis （PCA） method with a kernel trick to study the classification of phases and phase transitions in classical XY models of frustrated lattices. Compared to our previous work with the linear PCA method, the kernel PCA can capture nonlinear functions. In this case, the Z2 chiral order of the classical spins in these lattices is indeed a nonlinear function of the input spin configurations. In addition to the principal component revealed by the linear PCA, the kernel PCA can find two more principal components using the data generated by Monte Carlo simulation for various temperatures as the input. One of them is related to the strength of the U（1） order parameter, and the other directly manifests the chiral order parameter that characterizes the Z2 symmetry breaking. For a temperature-resolved study, the temperature dependence of the principal eigenvalue associated with the Z2 symmetry breaking clearly shows second-order phase transition behavior.
基金supported by the National Natural Science Foundation of China(11604225,11325418)Ministry of Science and Technology(2016YFA0301600)Foundation of Beijing Education Committees(KM201710028004)
文摘Recently an experiment on superradiant transition of a Bose condensate in two crossed beam cavities has been reported by Léonard et al. in Nature 543, 87(2017). The surprise is they find that across the superradiant transition, the cavity light can be emitted in any superposition of these two cavity modes. This indicates an additional U(1) symmetry that does not exist in the full Hamiltonian. In this paper we show that this symmetry is an emergent symmetry in the vicinity of the phase transition. We identify all the necessary conditions that are required for this emergent U(1) symmetry and show that this experiment is a special case that satisfies these conditions. We further show that the superradiant transition in this system can also be driven to a first order one when the system is tuned away from the point having the emergent symmetry.
基金supported by the National Natural Science Foundation of China(Grant No.11325418)
文摘Spin-orbit coupling is a relativistic effect for the charge particles such as electrons.It has been found that the spin-orbit coupling plays an important role in many branches of physics,for instance,in condensed matter physics,the spin-orbit cou-
基金supported by Beijing Outstanding Young Scholar Programthe National Key Research and Development Program of China (2021YFA0718303, 2021YFA1400904, and 2016YFA0301501)+1 种基金the National Natural Science Foundation of China (91736208, 11974202, 61975092, 11920101004,61727819, 11934002, 11734010, and 92165203)the XPLORER Prize。
文摘In 1970,Vitaly Efimov found an interesting phenomenon in a quantum three-body problem,which is now known as the Efimov effect.Efimov found that when the two-body in teraction potential is short-ranged and is tuned to the vicinity of an s-wave resonance,an inhnite number of three-body bound states emerge and their eigenenergies En form a geometric sequence as En=-|Eo|exp(—2m/So).
文摘The Efimov effect is defined as a quantum state with discrete scaling symmetry and a universal scaling factor. It has attracted considerable interests from nuclear to atomic physics communities. In a Dirac semi-metal, when an electron interacts with a static impurity through a Coulombic interaction, the same kinetic scaling and the interaction energy results in the Efimov effect. However, even when the Fermi energy lies exactly at the Dirac point, the vacuum polarization of the electron-hole pair fluctuation can still screen the Coulombic interaction, which leads to deviations from the scaling symmetry and eventually breaks down of the Efimov effect. This energy distortion of the Efimov states due to vacuum polarization is a relativistic electron analogy of the Lamb shift for the hydrogen atom. Motivated by the recent experimental observations in two- and three-dimensional Dirac semi-metals, we herein investigate this many-body correction to the Efimov effect and the conditions that allow some of the Efimov-like quasi-bound states to be observed in these condensed matter experiments.
基金supported by the Beijing Outstanding Young Scientist Program,Ministry of Science and Technology(Grant No.2016YFA0301600)the National Natural Science Foundation of China(Grant No.11734010)。
文摘The cocktail party problem refers to the phenomenon that the brain of a listener can focus on a single voice while filtering out a range of other voices in a multi-talker situation,say,in a cocktail party[1].This selective attention problem was firstly defined as the"cocktail party problem"(CPP)by Cherry[2]in 1953.In recent years,machine-learning based approaches to solve the CPP were essential for many industrial applications such as automated speech recognition.The independent component analysis(ICA)is such an algorithm particularly suitable for the CPP.The CPP also has applications in physical science such as astrophysics data analysis[3,4].
