Science China Physics, Mechanics & Astronomy最新文献

The bound states around a vortex in anisotropic superconductors is a longstanding yet important issue. In this work, we develop a variational theory on the basis of the Andreev approximation to obtain the energy levels and wave functions of the low-energy quantized bound states in superconductors with anisotropic pairing on arbitrary Fermi surface. In the case of circular Fermi surface, the effective Schrödinger equation yielding the bound state energies gets back to the theory proposed by Volovik and Kopnin many years ago. Our generalization here enables us to prove the equidistant energy spectrum inside a vortex in a broader class of superconductors. More importantly, we are now able to obtain the wave functions of these bound states by projecting the quasiclassical wave function on the eigenmodes of the effective Schrödinger equation, going beyond the quasiclassical Eilenberger results, which, as we find, are sensitive to the scattering rate. For the case of isotropic Fermi surface, the spatial profile of the low-energy local density of states is dominated near the vortex center and elongates along the gap antinode directions, in addition to the ubiquitous Friedel oscillation arising from the quantum inteference neglected in the Eilenberger theory. Moreover, as a consequence of the pairing anisotropy, the quantized wave functions develop a peculiar distribution of winding number, which reduces stepwise towards the vortex center. Our work provides a flexible way to study the vortex bound states in the future.

In topological insulators, massive surface states resulting from local symmetry breaking were thought to exhibit a half-quantized Hall conductance, obtained from the low-energy effective model in an infinite Brillouin zone. In a lattice model, the surface band is composed of a combination of surface states and bulk states. The massive surface states alone may not be enough to support an exact one-half quantized surface Hall conductance in a finite Brillouin zone and the whole surface band always gives an integer quantized Hall conductance as enforced by the TKNN theorem. To explore this, we investigate the band structures of a lattice model describing the magnetic topological insulator film that supports the axion insulator, Chern insulator, and semi-magnetic topological insulator phases. We reveal that the gapped and gapless surface bands in the three phases are characterized by an integer-quantized Hall conductance and a half-quantized Hall conductance, respectively. We propose an effective model to describe the three phases and show that the low-energy dispersion of the surface bands inherits from the surface Dirac fermions. The gapped surface band manifests a nearly half-quantized Hall conductance at low energy near the center of Brillouin zone, but is compensated by another nearly half-quantized Hall conductance at high energy near the boundary of Brillouin zone because a single band can only have an integer-quantized Hall conductance. The gapless band hosts a zero Hall conductance at low energy but is compensated by another half-quantized Hall conductance at high energy, and thus the half-quantized Hall conductance can only originate from the gapless band. Moreover, we calculate the layer-resolved Hall conductance of the system. The conclusion suggests that the individual gapped surface band alone does not support the half-quantized surface Hall effect in a lattice model.

Optical nonreciprocity, which refers to the direction-dependent emission, scattering and absorption of photons, plays a very important role in quantum engineering and quantum information processing. Here, we propose an all-optical approach to achieve the optical dynamical switchable quantum nonreciprocity by an off-resonant chiral two-photon driving in a single microring cavity, which differs from the conventional nonreciprocal schemes. It is shown that the optical field with time-dependent statistical properties can be generated and the nonreciprocity flips periodically, with switchable photon blockade and photon-induced tunneling effects. We find that the dynamical system is robust and immune to the parameter variations, which loosens the parameter range of system. Meanwhile, the time window for one-way quantum information is sufficiently wide and tunable. Our work opens a new idea for the current quantum nonreciprocal research, which can facilitate a memory functionality and be used for future in-memory superconducting quantum compute. The other nonreciprocal quantum devices, i.e., dynamical switchable nonreciprocal squeezing and entanglement, may be inspired by our method, which is expected to have important applications in future quantum technology.

We present a study on the energy radiation rate and waveforms of the gravitational wave generated by coalescing spinless binary systems up to the third post-Minkowskian approximation in the effective one-body theory. To derive an analytical expansion of the null tetrad components of the gravitational perturbed Weyl tensor Ψ₄ in the effective spacetime, we utilize the method proposed by Sasaki et al. During this investigation, we discover more general integral formulas that provide a theoretical framework for computing the results in any order. Subsequently, we successfully compute the energy radiation rate and waveforms of the gravitational wave, which include the results of the Schwarzschild case and the correction terms resulting from the dimensionless parameters a₂ and a₃ in the effective metric.

As the brightest gamma-ray burst ever observed, GRB 221009A provided a precious opportunity to explore spectral line features. In this article, we performed a comprehensive spectroscopy analysis of GRB 221009A jointly with GECAM-C and Fermi/GBM data to search for emission and absorption lines. For the first time we investigated the line feature throughout this GRB including the most bright part where many instruments suffered problems, and identified prominent emission lines in multiple time intervals. The central energy of the Gaussian emission line evolves from about 37 to 6 MeV, with a nearly constant ratio (about 10%) between the line width and central energy. Particularly, we find that both the central energy and the energy flux of the emission line evolve with time as a power law decay with power law index of −1 and −2, respectively. We suggest that the observed emission lines most likely origin from the blue-shifted electron positron pair annihilation 511 keV line. We find that a standard high latitude emission scenario cannot fully interpret the observation, thus we propose that the emission line comes from some dense clumps with electron positron pairs traveling together with the jet. In this scenario, we can use the emission line to directly, for the first time, measure the bulk Lorentz factor of the jet (Γ) and reveal its time evolution (i.e., Γ ∼ t⁻¹) during the prompt emission. Interestingly, we find that the flux of the annihilation line in the co-moving frame keeps constant. These discoveries of the spectral line features shed new and important lights on the physics of GRB and relativistic jet.

In the realm of modern information technology, data compression technology occupies a pivotal position. With advancements in quantum information technology, the need to compress large-scale qubits ensembles has become urgent, aiming to reduce the demand on quantum storage resources. However, existing quantum state compression schemes generally face a limitation: the particles before and after compression must reside in the same dimensional space. In specific scenarios, compressing qubits into particles of higher dimensions not only enhances the efficiency of quantum state compression but also further reduces the usage of quantum storage resources. Here we experimentally demonstrated a quantum state compression between particles of different dimensions, successfully compressing two qubits into a single qutrit. The average fidelity of the resulting qutrit with the ideal quantum state is 0.8835. Our study may have potential applications in future quantum information, such as increasing quantum communication bandwidth and reducing storage resource consumption in quantum computing.

Detecting the environment around the supermassive black holes and tests of general relativity are important applications of extreme-mass-ratio inspirals (EMRIs). There is still a challenge to efficiently describe various “dirty” impacts on the inspirals, such as dark matter, gas, dipole radiation, and electromagnetic interaction. In this study, we find the inherent linearity of the asymptotic solution of the inhomogeneous Teukolsky equation. On the basis of this property, we completely decouple the factors of the perturber and the background spacetime in the energy fluxes and waveforms. With the new decoupling form, the waveforms of EMRIs with non-geodesic motion in Kerr spacetime can be conveniently calculated. This will help to resolve the environment (including gas, field, dark matter, electromagnetic interaction) around supermassive black holes and test general relativity.

We present concrete evidence that Yang-Mills theory exhibits non-unitarity in non-integer spacetime dimensions. This violation of unitarity stems from evanescent operators that, while vanishing in four dimensions, are non-zero in general d dimensions. We demonstrate that these evanescent operators lead to the emergence of both negative-norm states and complex anomalous dimensions.

Lateral predictive coding is a recurrent neural network that creates energy-efficient internal representations by exploiting statistical regularity in sensory inputs. Here, we analytically investigate the trade-off between information robustness and energy in a linear model of lateral predictive coding and numerically minimize a free energy quantity. We observed several phase transitions in the synaptic weight matrix, particularly a continuous transition that breaks reciprocity and permutation symmetry and builds cyclic dominance and a discontinuous transition with the associated sudden emergence of tight balance between excitatory and inhibitory interactions. The optimal network follows an ideal gas law over an extended temperature range and saturates the efficiency upper bound of energy use. These results provide theoretical insights into the emergence and evolution of complex internal models in predictive processing systems.

In recent years, machine-learning methods have profoundly impacted research in the interdisciplinary fields of physics. However, most machine-learning models lack interpretability, and physicists doubt the credibility of their conclusions because they cannot be combined with prior physical knowledge. Therefore, this review focuses on symbolic regression, which is an interpretable machine-learning method. First, the relevant concepts of machine learning are introduced in conjunction with induction. Next, we provide an overview of symbolic regression methods. Subsequently, the recent directions for the application of symbolic regression methods in different subfields of physics are outlined, and an overview of the ways in which the applications of symbolic regression have evolved in the realm of physics is provided. The major aim of this review is to introduce the basic principles of symbolic regression and explain its applications in the field of physics.