arXiv subjects

Y. T. Liu

Publications and source records attributed to Y. T. Liu.

8 recordsLinked to original sources

arXiv2023

On relation between renormalized frequency and heat capacity for particles in an anharmonic potential

For free particles in a simple harmonic potential plus a weak anharmonicity, characterized by a set of anharmonic parameters, Newtonian mechanics asserts that there is a renormalization of the natural frequency of the periodic motion; and statistical mechanics claims that the anharmonicity causes a correction to the heat capacity of an ideal gas in the anharmonic potential. The orbital motion and thermal motion depend on the same anharmonic parameters, but in different combinations. These two manners of combinations are fundamentally different, demonstrating that statistical law can not emerge from the many-body limit of deterministic law for one-body.

cond-mat.stat-mech↗

arXiv2023

A correspondence from renormalized frequency to heat capacity for particles in an anharmonic potential

For particles in an anharmonic potential, classical mechanics asserts that there is a renormalization of the bare frequency of the oscillatory motion, and statistical mechanics claims that the anharmonicity causes a correction to the heat capacity of an ideal gas composed of particles in the anharmonic potential. When the frequency and the heat capacity are expressed in perturbative series, respective, in terms of the characteristic lengths in mechanics and statistical physics, the expansion coefficients have an order-by-order correspondence. This correspondence is in contrast to our intuition that the renormalized frequency enters the statistical mechanics as a single quantity.

cond-mat.stat-mech↗

arXiv2012

Weak ferrimagnetism and multiple magnetization reversal in α-Cr3(PO4)2

The chromium(II) orthophosphate α-Cr3(PO4)2 is a weak ferrimagnet with the Curie temperature TC = 29 K confirmed by a λ-type peak in specific heat. Dominant antiferromagnetic interactions in this system are characterized by the Weiss temperature Θ = - 96 K, indicating an intermediate frustration ratio |Θ|/TC ~ 3. In its magnetically ordered states α-Cr3(PO4)2 exhibits a remarkable sequence of temperature-induced magnetization reversals sensitive to the protocol of measurements, i.e. either field-cooled or zero-field-cooled regimes. The reduction of the effective magnetic moment 4.5 μB/Cr2+, as compared to the spin-only moment 4.9 μB/Cr2+, cannot be ascribed to the occurence of the low-spin state in any crystallographic site of the Jahn-Teller active 3d4 Cr2+ ions. X-ray absorption spectra at the K-edge indicate divalent chromium and unravel the high-spin state of these ions at the L2,3-edges. Weak ferrimagnetism and multiple magnetization reversal phenomena seen in this compound could be ascribed to incomplete cancellation and distortion of partial spontaneous magnetization functions of Cr2+ in its six crystallographically inequivalent positions.

cond-mat.mtrl-sci↗

arXiv2010

Dynamical spectral weight in YBa$_2$Cu$_3$O$_y$ probed by x-ray absorption spectroscopy

The comprehensive study of the temperature dependent x-ray absorption spectroscopy (XAS) reveals a dynamical spectral weight $α$ in YBa$_2$Cu$_3$O$_y$ (YBCO). Large spectral weight changes for both the Upper Hubbard band and the Zhang-Rice band due to dynamics of holes are experimentally found in the underdoped regime. A large value of $α\geq 0.3$ is indispensable to describing XAS of YBCO with the conservation of states. The value of $α$ is linearly proportional to the pseudogap temperature in the underdoped regime, but becomes smaller as the doping level goes to the undoped limit. Our results clearly indicate that the pseudogap is related to the double occupancy and originates from bands in higher energies.

cond-mat.str-el↗

arXiv2009

Equilibrium initial data for moving puncture simulations: The stationary 1+log slicing

We propose and explore a "stationary 1+log" slicing condition for the construction of solutions to Einstein's constraint equations. For stationary spacetimes, these initial data will give a stationary foliation when evolved with "moving puncture" gauge conditions that are often used in black hole evolutions. The resulting slicing is time-independent and agrees with the slicing generated by being dragged along a time-like Killing vector of the spacetime. When these initial data are evolved with moving puncture gauge conditions, numerical errors arising from coordinate evolution are minimized. In the construction of initial data for binary black holes it is often assumed that there exists an approximate helical Killing vector that generates the binary's orbit. We show that, unfortunately, 1+log slices that are stationary with respect to such a helical Killing vector cannot be asymptotically flat, unless the spacetime possesses an additional axial Killing vector.

gr-qc↗

arXiv1999

Perturbative Approach to the Quasinormal Modes of Dirty Black Holes

Using a recently developed perturbation theory for uasinormal modes (QNM's), we evaluate the shifts in the real and imaginary parts of the QNM frequencies due to a quasi-static perturbation of the black hole spacetime. We show the perturbed QNM spectrum of a black hole can have interesting features using a simple model based on the scalar wave equation.

gr-qc↗

arXiv1999

Quasinormal Modes of Dirty Black Holes

Quasinormal mode (QNM) gravitational radiation from black holes is expected to be observed in a few years. A perturbative formula is derived for the shifts in both the real and the imaginary part of the QNM frequencies away from those of an idealized isolated black hole. The formulation provides a tool for understanding how the astrophysical environment surrounding a black hole, e.g., a massive accretion disk, affects the QNM spectrum of gravitational waves. We show, in a simple model, that the perturbed QNM spectrum can have interesting features.

gr-qc↗

arXiv1997

Logarithmic perturbation theory for quasinormal modes

Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states is not required. Attention is paid to potentials with exponential tails, and the example of a Poschl-Teller potential is briefly discussed. A numerical method is developed that handles the exponentially large wavefunctions which appear in dealing with QNMs.

math-ph↗