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C. Ford

Publications and source records attributed to C. Ford.

15 recordsLinked to original sources
arXiv2019

Preserving orbital order in a layered manganite by ultrafast hybridized band excitation

In the mixed-valence manganites, a near-infrared laser typically melts the orbital and spin order simultaneously, corresponding to the photoinduced $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ excitations in the Mott-Hubbard bands of manganese. Here, we use ultrafast methods -- both femtosecond resonant x-ray diffraction and optical reflectivity -- to demonstrate that the orbital response in the layered manganite Nd$_{1-x}$Sr$_{1+x}$MnO$_{4}$ ($\it{x}$ = 2/3) does not follow this scheme. At the photoexcitation saturation fluence, the orbital order is only diminished by a few percent in the transient state. Instead of the typical $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ transition, a near-infrared pump in this compound promotes a fundamentally distinct mechanism of charge transfer, the $d^{0}$ $ \xrightarrow{}$ $d^{1}L$, where $\it{L}$ denotes a hole in the oxygen band. This novel finding may pave a new avenue for selectively manipulating specific types of order in complex materials of this class.

cond-mat.str-el↗
arXiv2000

ADHM Construction of Instantons on the Torus

We apply the ADHM instanton construction to SU(2) gauge theory on T^n x R^(4-n)for n=1,2,3,4. To do this we regard instantons on T^n x R^(4-n) as periodic (modulo gauge transformations) instantons on R^4. Since the R^4 topological charge of such instantons is infinite the ADHM algebra takes place on an infinite dimensional linear space. The ADHM matrix M is related to a Weyl operator (with a self-dual background) on the dual torus tilde T^n. We construct the Weyl operator corresponding to the one-instantons on T^n x R^(4-n). In order to derive the self-dual potential on T^n x R^(4-n) it is necessary to solve a specific Weyl equation. This is a variant of the Nahm transformation. In the case n=2 (i.e. T^2 x R^2) we essentially have an Aharonov Bohm problem on tilde T^2. In the one-instanton sector we find that the scale parameter, lambda, is bounded above, (lambda)^2 tv<4 pi, tv being the volume of the dual torus tilde T^2.

hep-th↗
arXiv1998

SU(N)-Gauge Theories in Polyakov Gauge on the Torus

We investigate the Abelian projection with respect to the Polyakov loop operator for SU(N) gauge theories on the four torus. The gauge fixed $A_0$ is time-independent and diagonal. We construct fundamental domains for $A_0$. In sectors with non-vanishing instanton number such gauge fixings are always singular. The singularities define the positions of magnetically charged monopoles, strings or walls. These magnetic defects sit on the Gribov horizon and have quantized magnetic charges. We relate their magnetic charges to the instanton number.

hep-th↗
arXiv1998

Abelian Projection on the Torus for general Gauge Groups

We consider Yang-Mills theories with general gauge groups $G$ and twists on the four torus. We find consistent boundary conditions for gauge fields in all instanton sectors. An extended Abelian projection with respect to the Polyakov loop operator is presented, where $A_0$ is independent of time and in the Cartan subalgebra. Fundamental domains for the gauge fixed $A_0$ are constructed for arbitrary gauge groups. In the sectors with non-vanishing instanton number such gauge fixings are necessarily singular. The singularities can be restricted to Dirac strings joining magnetically charged defects. The magnetic charges of these monopoles take their values in the co-root lattice of the gauge group. We relate the magnetic charges of the defects and the windings of suitable Higgs fields about these defects to the instanton number.

hep-th↗
arXiv1998

Monopoles, Polyakov-Loops and Gauge Fixing on the Torus

We consider pure Yang Mills theory on the four torus. A set of non-Abelian transition functions is presented which encompass all instanton sectors. It is argued that these transition functions are a convenient starting point for gauge fixing. In particular, we give an extended Abelian projection with respect to the Polyakov loop, where $A_0$ is independent of time and in the Cartan subalgebra. In the non-perturbative sectors such gauge fixings are necessarily singular. These singularities can be restricted to Dirac strings joining monopole and anti-monopole like ``defects''.

hep-th↗
arXiv1996

Multi-scale Renormalization

The Standard MS renormalization prescription is inadequate for dealing with multi-scale problems. To illustrate this we consider the computation of the effective potential in the Higgs-Yukawa model. It is argued that it is natural to employ a two-scale renormalization group. We give a modified version of a two-scale scheme introduced by Einhorn and Jones. In such schemes the beta functions necessarily contain potentially large logarithms of the RG scale ratios. For credible perturbation theory one must implement a large logarithms resumation on the beta functions themselves. We show how the integrability condition for the two RG equations allows one to perform this resummation.

hep-th↗
arXiv1996

A Multi-scale Subtraction Scheme and Partial Renormalization Group Equations in the $O(N)$-symmetric $ϕ^4$-theory

To resum large logarithms in multi-scale problems a generalization of $\MS$ is introduced allowing for as many renormalization scales as there are generic scales in the problem. In the new \lq\lq minimal multi-scale subtraction scheme'' standard perturbative boundary conditions become applicable. However, the multi-loop beta functions depend on the various renormalization scale ratios and a large logarithms resummation has to be performed on them. Using these improved beta functions the \lq\lq partial'' renormalization group equations corresponding to the renormalization point independence of physical quantities allows one to resum the logarithms. As an application the leading and next-to-leading order two-scale analysis of the effective potential in the $O(N)$-symmetric $ϕ^4$-theory is performed. This calculation indicates that there is no stable vacuum in the broken phase of the theory for $1<N\leq4$.

hep-ph↗
arXiv1995

Canonical Quantization of Interacting WZW Theories

Using canonical quantization we find the Virasoro centre for a class of conformally-invariant interacting Wess-Zumino-Witten theories. The theories have a group structure similar to that of Toda theories (both abelian and non-abelian) but the usual Toda constraints on the coupling constants are relaxed and the theories are not necessarily integrable. The general formula for the Virasoro centre is compared to that derived by BRST methods in the Toda case, and helps to explain the structure of the latter.

hep-th↗
arXiv1995

Duality and the Legendre Transform

We define a weak-strong coupling transformation based on the Legendre transformation of the effective action. In the case of $N\es 2$ supersymmetric Yang-Mills theory, this coincides with the duality transform on the low energy effective action considered by Seiberg and Witten. This Legendre transform interpretation of duality generalizes directly to the full effective action, and in principle to other theories.

hep-th↗
arXiv1992

The effective potential and the renormalisation group

We discuss renormalisation group improvement of the effective potential both in general and in the context of $O(N)$ scalar $\p^4$ and the Standard Model. In the latter case we find that absolute stability of the electroweak vacuum implies that $m_H\geq 1.95m_t-189~GeV$, for $\as (M_Z) = 0.11$. We point out that the lower bound on $m_H$ {\it decreases\/} if $\as (M_Z)$ is increased.

hep-lat↗