publications

2024

1. arxiv

   Is the finite temperature effective potential, effective for dynamics?

   Nathan Herring, Shuyang Cao, and Daniel Boyanovsky

   Oct 2024

   Abs arXiv Bib

   We study the applicability of the finite temperature effective potential in the equation of motion of a homogeneous “misaligned” scalar condensate \varphi, and find important caveats that severely restrict its domain of validity: \textbackslashtextbf{i:)} the \textbackslashemph{assumption} of local thermodynamic equilibrium (LTE) is in general not warranted, \textbackslashtextbf{ii:)} we show a direct relation between the effective potential and the thermodynamic entropy density \mathcal{S}= - ∂V_{eff}(T,\varphi)/∂T, which entails that for a dynamical \varphi(t) the entropy becomes a non-monotonic function of time, \textbackslashtextbf{iii:)} parametric instabilities in both cases with and without spontaneous symmetry breaking lead to profuse particle production with non-thermal distribution functions, \textbackslashtextbf{iv:)} in the case of spontaneous symmetry breaking spinodal instabilities yield a complex effective potential, internal energy and \textbackslashemph{entropy}, an untenable situation in thermodynamics. All these caveats associated with dynamical aspects, cannot be overcome by finite temperature equilibrium resummation schemes. We argue that the dynamics of the condensate leads to decoupling and freeze-out from (LTE), and propose a \textbackslashemph{closed} quantum system approach based on unitary time evolution. It yields the correct equations of motion without the caveats of the effective potential, and provides a fully renormalized and thermodynamically consistent framework to study the dynamics of the “misaligned” condensate, with real and conserved energy and entropy amenable to numerical study. The evolution of the condensate leads to profuse \textbackslashemph{stimulated particle production} with non-thermal distribution functions. Possible emergent asymptotic non-thermal states and eventual re-thermalization are conjectured.

   @article{Herring2024-pt,
     title = {Is the finite temperature effective potential, effective for dynamics?},
     author = {Herring, Nathan and Cao, Shuyang and Boyanovsky, Daniel},
     month = oct,
     year = {2024},
     copyright = {http://arxiv.org/licenses/nonexclusive-distrib/1.0/},
     archiveprefix = {arXiv},
     primaryclass = {hep-ph},
     eprint = {2410.21633}
   }

2. arxiv

   Condensate decay in a radiation dominated cosmology

   Shuyang Cao, and Daniel Boyanovsky

   Sep 2024

   Abs arXiv Bib

   We study the decay of a homogeneous condensate of a massive scalar field of mass \textbackslashemph{m} into massless fields in thermal equilibrium in a radiation dominated cosmology. The model is a \textbackslashemph{proxy} for the non-equilibrium dynamics of a misaligned axion condensate decaying into radiation. After consistent field quantization in the cosmological background, we obtain the causal equations of motion for a homogeneous condensate including the finite temperature self-energy corrections up to one loop. The dynamical renormalization group is implemented to obtain the time dependent relaxation rate that describes the decay dynamics of the condensate amplitude from stimulated emission and recombination of massless quanta in the medium. It is explicitly shown that a simple friction term in the equation of motion does not describe correctly the decay of the condensate. During the super-Hubble regime, relevant for ultralight dark matter, the condensate amplitude decays as e^{-\frac{g^2}{10} t^2\,\ln(1/mt)}. In the sub-Hubble regime the amplitude decays as e^{-γ(t;T(t))/2} with T(t)=T_0/a(t), therefore the finite temperature contribution to the decay rate vanishes fast during the expansion. A main conclusion is that a phenomenological friction term is inadequate to describe the decay in the super-Hubble regime, the decay function γ(t) is always \textbackslashemph{smaller} than that from a local friction term as a consequence of the cosmological expansion. For ultra light dark matter, the time scale during which transient dynamics is sensitive to cosmological expansion and a local friction term is inadequate, is much longer. A friction term always \textbackslashemph{underestimates} the time scale of decay in the sub-Hubble case.

   @article{Cao2024-kq,
     title = {Condensate decay in a radiation dominated cosmology},
     author = {Cao, Shuyang and Boyanovsky, Daniel},
     month = sep,
     year = {2024},
     copyright = {http://arxiv.org/licenses/nonexclusive-distrib/1.0/},
     archiveprefix = {arXiv},
     primaryclass = {hep-th},
     eprint = {2409.16076},
     keywords = {submitted}
   }

3. arxiv

   Field mixing in a thermal medium: A quantum master equation approach

   Shuyang Cao

   Aug 2024

   Abs arXiv Bib

   We studied the nonequilibrium dynamics of the indirect mixing of two (pseudo-)scalar fields induced by their couplings to common decay channels in a medium. The effective non-Markovian quantum master equation (QME) for the two fields’ reduced density matrix is derived to leading order in the couplings of the two fields with the medium, but to all orders of the couplings among degrees of freedom in the medium. The self-energy and noise-kernel in the QME satisfy a fluctuation-dissipation relation. The solutions show that an initial expectation value (condensate) of one field induces a condensate of the other field through the indirect mixing and that the populations and coherence of the two fields thermalize and approach to non-vanishing values asymptotically. The nearly-degenerate field masses and coupling strengths resonantly enhance the quantum beats and asymptotic coherence, and induce a prominent dynamics of the vacuum after the switch-on of the couplings. We argue that a time-dependent definitions of particles due to the changing vacuum must be introduced so as to obtain results consistent with the calculations of equilibrium states in the asymptotic limit. A coupling strength hierarchy breaks down the resonant enhancement in the nearly-degenerate case but leads to different power countings of the coupling strengths in the magnitudes of the observables and time-scales in the evolution, suggesting the possibility of detecting extremely long-lived particles using prepared short-lived particles within a practical experimental period.

   @article{cao2024fieldmixingthermalmedium,
     title = {Field mixing in a thermal medium: A quantum master equation approach},
     author = {Cao, Shuyang},
     month = aug,
     year = {2024},
     eprint = {2408.08460},
     archiveprefix = {arXiv},
     primaryclass = {quant-ph},
     url = {https://arxiv.org/abs/2408.08460}
   }

4. PhysRevD

   Is the effective potential effective for dynamics?

   Nathan Herring, Shuyang Cao, and Daniel Boyanovsky

   Phys. Rev. D, May 2024

   Abs arXiv Bib HTML

   We critically examine the applicability of the effective potential within dynamical situations and find, in short, that the answer is negative. An important caveat of the use of an effective potential in dynamical equations of motion is an explicit violation of energy conservation. An \emphadiabatic effective potential is introduced in a consistent quasi-static approximation, and its narrow regime of validity is discussed. Two ubiquitous instances in which even the adiabatic effective potential is not valid in dynamics are studied in detail: parametric amplification in the case of oscillating mean fields, and spinodal instabilities associated with spontaneous symmetry breaking. In both cases profuse particle production is directly linked to the failure of the effective potential to describe the dynamics. We introduce a consistent, renormalized, energy conserving dynamical framework that is amenable to numerical implementation. Energy conservation leads to the emergence of asymptotic highly excited, entangled stationary states from the dynamical evolution. As a corollary, decoherence via dephasing of the density matrix in the adiabatic basis is argued to lead to an emergent entropy, formally equivalent to the entanglement entropy. The results suggest novel characterization of asymptotic equilibrium states in terms of order parameter vs. energy density.

   @article{PhysRevD.109.105021,
     title = {Is the effective potential effective for dynamics?},
     author = {Herring, Nathan and Cao, Shuyang and Boyanovsky, Daniel},
     journal = {Phys. Rev. D},
     volume = {109},
     issue = {10},
     pages = {105021},
     numpages = {27},
     year = {2024},
     month = may,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevD.109.105021},
     url = {https://link.aps.org/doi/10.1103/PhysRevD.109.105021},
     eprint = {2403.07084},
     archiveprefix = {arXiv},
     primaryclass = {hep-ph}
   }

5. PhysRevD

   Effective field theory of particle mixing

   Shuyang Cao, and Daniel Boyanovsky

   Phys. Rev. D, Feb 2024

   Abs arXiv Bib HTML

   We introduce an effective field theory to study indirect mixing of two fields induced by their couplings to a common decay channel in a medium. The extension of the method of Lee, Oehme, and Yang, the cornerstone of analysis of CP violation in flavored mesons, to include the mixing of particles with different masses provides a guide to and benchmark for the effective field theory. The analysis reveals subtle caveats in the description of mixing in terms of the widely used non-Hermitian effective Hamiltonian, more acute in the nondegenerate case. The effective field theory describes the dynamics of field mixing where the common intermediate states populate a bath in thermal equilibrium, as an open quantum system. We obtain the effective action up to second order in the couplings, where indirect mixing is a consequence of off-diagonal self-energy components. We find that if only one of the mixing fields features an initial expectation value, indirect mixing induces an expectation value of the other field. The equal time two point correlation functions exhibit an asymptotic approach to a stationary thermal state, and the emergence of long-lived bath-induced coherence which displays quantum beats as a consequence of interference of quasinormal modes in the medium. The amplitudes of the quantum beats are resonantly enhanced in the nearly degenerate case with potential observational consequences.

   @article{PhysRevD.109.036038,
     title = {Effective field theory of particle mixing},
     author = {Cao, Shuyang and Boyanovsky, Daniel},
     journal = {Phys. Rev. D},
     volume = {109},
     issue = {3},
     pages = {036038},
     numpages = {33},
     year = {2024},
     month = feb,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevD.109.036038},
     url = {https://link.aps.org/doi/10.1103/PhysRevD.109.036038},
     eprint = {2310.17070},
     archiveprefix = {arXiv},
     primaryclass = {hep-ph}
   }

2023

1. PhysRevD

   Dynamics of axion-neutral pseudoscalar mixing

   Shuyang Cao, Wenjie Huang, and Daniel Boyanovsky

   Phys. Rev. D, Jul 2023

   Abs arXiv Bib HTML

   Axions mix with neutral pions after the QCD phase transition through their common coupling to the radiation bath via a Chern-Simons term, as a consequence of the U(1) anomaly. The non-equilibrium effective action that describes this mixing phenomenon is obtained to second order in the coupling of neutral pions and axions to photons. We show that a misaligned axion condensate induces a neutral pion condensate after the QCD phase transition. The dynamics of the pion condensate displays long and short time scales and decays on the longer time scale exhibiting a phenomenon akin to the “purification” in a Kaon beam. On the intermediate time scales the macroscopic pion condensate is proportional to a condensate of the abelian Chern-Simons term induced by the axion. We argue that the coupling to the common bath also induces kinetic mixing. We obtain the axion and pion populations, and these exhibit thermalization with the bath. The mutual coupling to the bath induces long-lived axion- neutral pion coherence independent of initial conditions. The framework of the effective action and many of the consequences are more broadly general and applicable to scalar or pseudoscalar particles mixing in a medium.

   @article{PhysRevD.108.025012,
     title = {Dynamics of axion-neutral pseudoscalar mixing},
     author = {Cao, Shuyang and Huang, Wenjie and Boyanovsky, Daniel},
     journal = {Phys. Rev. D},
     volume = {108},
     issue = {2},
     pages = {025012},
     numpages = {20},
     year = {2023},
     month = jul,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevD.108.025012},
     url = {https://link.aps.org/doi/10.1103/PhysRevD.108.025012},
     archiveprefix = {arXiv},
     eprint = {2304.13884}
   }

2. PhysRevD

   Chern Simons condensate from misaligned axions

   Shuyang Cao, and Daniel Boyanovsky

   Phys. Rev. D, Apr 2023

   Abs arXiv Bib HTML

   We obtain the non-equilibrium condensate of the Chern Simons density induced by a misaligned homogeneous coherent axion field in linear response. The Chern-Simons dynamical susceptibility is simply related to the axion self-energy, a result that is valid to leading order in the axion coupling but to all orders in the couplings of the gauge fields to other fields within or beyond the standard model except the axion. The induced Chern-Simons density requires renormalization which is achieved by vacuum subtraction. For ultralight axions of mass m_a coupled to electromagnetic fields with coupling g, the renormalized high temperature contribution post-recombination is ⟨\vecE⋅\vecB⟩(t) = -\fracg\,\pi^2 T^415 \,\overlinea(t)+ \fracg  m^2_a T16\,\pi\,\dot\overlinea(t) with \overlinea(t) the dynamical homogeneous axion condensate. We conjecture that emergent axion-like quasiparticle excitations in condensed matter systems may be harnessed to probe cosmological axions and the Chern-Simons condensate. Furthermore, it is argued that a misaligned axion can also induce a non-abelian Chern-Simons condensate of similar qualitative form, and can also “seed” chiral symmetry breaking and induce a neutral pion condensate after the QCD phase transition.

   @article{PhysRevD.107.083531,
     title = {Chern Simons condensate from misaligned axions},
     author = {Cao, Shuyang and Boyanovsky, Daniel},
     journal = {Phys. Rev. D},
     volume = {107},
     issue = {8},
     pages = {083531},
     numpages = {14},
     year = {2023},
     month = apr,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevD.107.083531},
     url = {https://link.aps.org/doi/10.1103/PhysRevD.107.083531},
     archiveprefix = {arXiv},
     eprint = {2303.04197}
   }

3. PhysRevD

   Nonequilibrium dynamics of axionlike particles: The quantum master equation

   Shuyang Cao, and Daniel Boyanovsky

   Phys. Rev. D, Mar 2023

   Abs arXiv Bib HTML

   We study the non-equilibrium dynamics of Axion-like particles (ALP) coupled to Standard Model degrees of freedom in thermal equilibrium. The Quantum Master Equation (QME) for the (ALP) reduced density matrix is derived to leading order in the coupling of the (ALP) to the thermal bath, but to \textbackslashemph{all} orders of the bath couplings to degrees of freedom within or beyond the Standard Model other than the (ALP). The (QME) describes the damped oscillation dynamics of an initial misaligned (ALP) condensate, thermalization with the bath, decoherence and entropy production within a unifying framework. The (ALP) energy density \mathcal{E}(t) features two components: a “cold” component from the misaligned condensate and a “hot” component from thermalization with the bath, with \mathcal{E}(t)=\mathcal{E}_{c} e^{-γ(T) t}+\mathcal{E}_{h}(1-e^{-γ(T) t}) thus providing a “mixed dark matter” scenario. Relaxation of the (ALP) condensate, thermalization, decoherence and entropy production occur on similar time scales. An explicit example with (ALP)-photon coupling, valid post recombination yields a relaxation rate γ(T) with a substantial enhancement from thermal emission and absorption. A misaligned condensate is decaying at least since recombination and on the same time scale thermalizing with the cosmic microwave background (CMB). Possible consequences for birefringence of the (CMB) and (ALP) contribution to the effective number of ultrarelativistic species and galaxy formation are discussed.

   @article{PhysRevD.107.063518,
     title = {Nonequilibrium dynamics of axionlike particles: The quantum master equation},
     author = {Cao, Shuyang and Boyanovsky, Daniel},
     journal = {Phys. Rev. D},
     volume = {107},
     issue = {6},
     pages = {063518},
     numpages = {15},
     year = {2023},
     month = mar,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevD.107.063518},
     url = {https://link.aps.org/doi/10.1103/PhysRevD.107.063518},
     archiveprefix = {arXiv},
     primaryclass = {astro-ph.CO},
     eprint = {2212.05161}
   }

2022

1. PhysRevD

   Brownian axionlike particles

   Shuyang Cao, and Daniel Boyanovsky

   Phys. Rev. D, Dec 2022

   Abs arXiv Bib HTML

   We study the non-equilibrium dynamics of a pseudoscalar axion-like particle (ALP) weakly coupled to degrees of freedom in thermal equilibrium by obtaining its reduced density matrix. Its time evolution is determined by the in-in effective action which we obtain to leading order in the (ALP) coupling but to \emphall orders in the couplings of the bath to other fields within or beyond the standard model. The effective equation of motion for the (ALP) is a Langevin equation with noise and friction kernels obeying the fluctuation dissipation relation. A “misaligned” initial condition yields damped coherent oscillations, however, the (ALP) population increases towards thermalization with the bath. As a result, the energy density features a mixture of a cold component from misalignment and a hot component from thermalization with proportions that vary in time (cold) e^-Γt+(hot)\,(1-e^-Γt), providing a scenario wherein the “warmth” of the dark matter evolves in time from colder to hotter. As a specific example we consider the (ALP)-photon coupling g a \vecE⋅\vecB to lowest order, valid from recombination onwards. For T ≫m_a the long-wavelength relaxation rate is substantially enhanced \Gamma_T = \fracg^2 m^2_a T16\pi . The ultraviolet divergences of the (ALP) self-energy require higher order derivative terms in the effective action. We find that at high temperature, the finite temperature effective mass of the (ALP) is m^2_a(T) = m^2_a(0)\Big[ 1-(T/T_c)^4\Big], with T_c ∝\sqrtm_a(0)/g, \emphsuggesting the possibility of an inverted phase transition, which when combined with higher derivatives may possibly indicate exotic new phases. We discuss possible cosmological consequences on structure formation, the effective number of relativistic species and birefringence of the cosmic microwave background.

   @article{PhysRevD.106.123503,
     title = {Brownian axionlike particles},
     author = {Cao, Shuyang and Boyanovsky, Daniel},
     journal = {Phys. Rev. D},
     volume = {106},
     issue = {12},
     pages = {123503},
     numpages = {24},
     year = {2022},
     month = dec,
     publisher = {American Physical Society},
     doi = {10.1103/PhysRevD.106.123503},
     url = {https://link.aps.org/doi/10.1103/PhysRevD.106.123503},
   }

2019

1. Opt. Express

   Extraction and identification of noise patterns for ultracold atoms in an optical lattice

   Shuyang Cao, Pengju Tang, Xinxin Guo, Xuzong Chen, Wei Zhang, and Xiaoji Zhou

   Opt. Express, Apr 2019

   Abs arXiv Bib HTML

   To extract useful information about quantum effects in cold atom experiments, one central task is to identify the intrinsic fluctuations from extrinsic system noises of various kinds. As a data processing method, principal component analysis can decompose fluctuations in experimental data into eigenmodes, and give a chance to separate noises originated from different physical sources. In this paper, we demonstrate for Bose-Einstein condensates in one-dimensional optical lattices that the principal component analysis can be applied to time-of-flight images to successfully separate and identify noises from different origins of leading contribution, and can help to reduce or even eliminate noises via corresponding data processing procedures. The attribution of noise modes to their physical origins is also confirmed by numerical analysis within a mean-field theory. As the method does not rely on any a priori knowledge of the system properties, it is potentially applicable to the study of other quantum states and quantum critical regions.

   @article{Cao:19,
     author = {Cao, Shuyang and Tang, Pengju and Guo, Xinxin and Chen, Xuzong and Zhang, Wei and Zhou, Xiaoji},
     journal = {Opt. Express},
     keywords = {Coherent states; Gaussian beams; Numerical simulation; Optical lattices; Optical potentials; Photon counting},
     number = {9},
     pages = {12710--12722},
     publisher = {OSA},
     title = {Extraction and identification of noise patterns for ultracold atoms in an optical lattice},
     volume = {27},
     month = apr,
     year = {2019},
     url = {http://www.opticsexpress.org/abstract.cfm?URI=oe-27-9-12710},
     doi = {10.1364/OE.27.012710}
   }

2017

1. ChinPhysLett

   Coupled Two-Dimensional Atomic Oscillation in an Anharmonic Trap

   Dong Hu, Lin-Xiao Niu, Jia-Hua Zhang, Xin-Hao Zou, Shu-Yang Cao, and Xiao-Ji Zhou

   Chinese Physics Letters, Jul 2017

   Abs Bib HTML

   In atomic dynamics, oscillation along different axes can be studied separately in the harmonic trap. When the trap is not harmonic, motion in different directions may couple together. In this work, we observe a two-dimensional oscillation by exciting atoms in one direction, where the atoms are transferred to an anharmonic region. Theoretical calculations are coincident to the experimental results. These oscillations in two dimensions not only can be used to measure trap parameters but also have potential applications in atomic interferometry and precise measurements.

   @article{Hu_2017,
     doi = {10.1088/0256-307x/34/7/076701},
     url = {https://doi.org/10.1088%2F0256-307x%2F34%2F7%2F076701},
     year = {2017},
     month = jul,
     publisher = {{IOP} Publishing},
     volume = {34},
     number = {7},
     pages = {076701},
     author = {Hu, Dong and Niu, Lin-Xiao and Zhang, Jia-Hua and Zou, Xin-Hao and Cao, Shu-Yang and Zhou, Xiao-Ji},
     title = {Coupled Two-Dimensional Atomic Oscillation in an Anharmonic Trap},
     journal = {Chinese Physics Letters}
   }