Pei Wang

We develop a Schrödinger-picture formulation for a scalar quantum field driven by a Lorentz-invariant white-noise field. The quantum state of the system is described by a stochastic wave functional that evolves according to a stochastic Schrödinger equation. We show that the Gaussian structure of the wave functional is preserved under the stochastic evolution, allowing the dynamics to be reduced to a set of equations for the corresponding kernel functions. These kernel equations are derived and solved exactly, yielding an explicit time-dependent expression for the wave functional. The exact solution enables a direct analysis of the statistical properties of the quantum field in the space of field configurations. In particular, we show that the expectation value of the field operator obeys the same stochastic equation as the classical field obtained from the Euler–Lagrange equation of the action. We further compute the energy density from the stochastic wave functional and evaluate its ensemble average over noise realizations. The resulting energy production rate coincides with that obtained from the corresponding Lindblad equation. This result indicates that the stochastic quantum state remains well defined even though certain derived observables exhibit ultraviolet divergences associated with the white-noise idealization.

We investigate a relativistic stochastic field theory in which a complex scalar doublet is coupled to a complex white-noise source. The action preserves Lorentz and U ( 1 ) × SU ( 2 ) symmetries at the statistical level, whereas the corresponding Euler–Lagrange equations exhibit symmetry breaking along individual stochastic realizations. Within a gauge-field-free sector introduced to obtain analytical solutions, we show that the scalar doublet undergoes a noise-driven random walk in field space, leading to a finite, time-dependent ensemble average of its magnitude. As an illustrative application, we further investigate the coupling of the stochastic scalar field to fermions through a Yukawa interaction. The scalar-field solution naturally separates into a tail component, which contributes as an effective mass-like term, and a light-cone component, which acts as a colored-noise source that induces a spatially correlated stochastic phase in the fermion wave function. The statistical properties and correlation length of this emergent colored noise are derived analytically within the adopted approximations. The present work provides an exploratory study of statistical symmetry breaking and emergent colored-noise dynamics in a relativistic stochastic scalar-doublet field theory.

We develop a quantum field theory based on random nonHermitian actions, which upon quantization lead to stochastic nonlinear Schrödinger dynamics for the state vector. In this framework, Lorentz and spacetime translation symmetries are preserved only in a statistical sense: the probability distribution of the action remains invariant under these transformations. As a result, the theory describes ensembles of quantum-state trajectories whose probability distributions remain invariant under changes of reference frame. As a concrete example, we augment the Dirac action with a purely imaginary term coupling the fermion density operator to a universal colored noise. This noise is constructed by solving the d’Alembert equation with white noise as its source, using a generalized stochastic calculus in 1+3 dimensions. We demonstrate that the colored noise drives stochastic localization of wave packets and derive the localization length analytically. Remarkably, the localization length decreases as the size of the observable universe increases. Our model thus provides a potential framework for relativistic spontaneous wave-function collapse. While establishing consistency with Born’s law remains an open challenge, the present work constitutes a step toward embedding collapse models into a Lorentz-invariant quantum field theory.

We develop a theory of random non-Hermitian action that, after quantization, describes the stochastic nonlinear dynamics of quantum states in Hilbert space. Focusing on fermionic fields, we propose both canonical quantization and path integral quantization, demonstrating that these two approaches are equivalent. Using this formalism, we investigate the evolution of a single-particle Gaussian wave packet under the influence of non-Hermiticity and randomness. Our results show that specific types of non-Hermiticity lead to wave packet localization, while randomness affects the central position of the wave packet, causing the variance of its distribution to increase with the strength of the randomness.

We develop a theory of random non-Hermitian action that, after quantization, describes the stochastic nonlinear dynamics of quantum states in Hilbert space. Focusing on fermionic fields, we propose both canonical quantization and path integral quantization, demonstrating that these two approaches are equivalent. Using this formalism, we investigate the evolution of a single-particle Gaussian wave packet under the influence of non-Hermiticity and randomness. Our results show that specific types of non-Hermiticity lead to wave packet localization, while randomness affects the central position of the wave packet, causing the variance of its distribution to increase with the strength of the randomness.

We apply a state-of-the-art difference-in-differences approach to estimate the impact of ChatGPT's release on the writing style of condensed matter papers on arXiv. Our analysis reveals a statistically significant improvement in the English quality of abstracts written by non-native English speakers. Importantly, this improvement remains robust even after accounting for other potential factors, confirming that it can be attributed to the release of ChatGPT. This indicates widespread adoption of the tool. Following the release of ChatGPT, there is a significant increase in the use of unique words, while the frequency of rare words decreases. Across language families, the changes in writing style are significant for authors from the Latin and Ural-Altaic groups, but not for those from the Germanic or other Indo-European groups.

We present a phenomenological model for magnetoelectricity in multiferroic materials. The distinctive feature of the model is a two-component complex order parameter that encodes the electric polarization, along with a direct coupling between the polarization and magnetic field. Our model effectively elucidates that a sufficiently strong magnetic field can destroy electric polarization. Furthermore, the transition field strength diminishes with rising temperature, following a power-law relation with the exponent being precisely worked out. At lower field strength, the electric polarization takes a spiral order in the magnetic field, with the spiral wavelength inversely proportional to the magnetic field strength. We anticipate these predictions can be experimentally tested in future studies on multiferroic materials.

We study the all-to-all Ising model in the presence of dissipation and periodic external field. The corresponding Lindblad equation has a time-periodic Liouvillian. The dynamics of magnetizations is explored by using both the mean-field theory and numerical simulation at a finite number of spins. The mean-field result exhibits a transition from the periodic response at small field amplitude to the chaotic dynamics at large amplitude. The Lyapunov exponents are calculated, which supports the existence of a classical chaotic phase. However, in the numerical simulation at a finite number of spins, the response is periodic at both small and large amplitudes. The scaling analysis of the Floquet Liouvillian spectrum suggests that the periodic response persists even in the thermodynamic limit. Further analysis shows that, in the classical chaotic regime, the density-matrix elements have a wide dispersion, instead of being localized. Such a delocalization of wave packets explains the failure of mean-field approximation.

We discover a class of spacetime symmetries unique to time-periodic systems, which we term “mixing symmetry” due to its combination of space and time coordinates in the symmetry transformation. We systematically enumerate the symmetry groups and classify the corresponding Floquet-Bloch band theories by utilizing the winding number of quasienergy. Moreover, we provide a comprehensive scheme for the experimental realization of these symmetries. The particle propagator exhibits an intriguing pattern that remains invariant even under transformations mixing space and time coordinates. We anticipate that this distinct feature can be observed in current cold atom experiments.