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首页自发破译:电荷密度下的非相干传输与黑洞热电性质
本文主要探讨了自发打破空间平移的有限电荷密度物质相中的非相干传输现象。作者Aristomenis Donos、Jerome P. Gauntlett、Tom Griffin和Vaios Ziogas来自英国杜伦大学粒子理论中心和数学科学系以及帝国理工学院的布莱克特实验室,他们研究了在不采用流体动力学极限的前提下,物质系统如何处理这种非对称性。 核心成果是确定了一个在boost不变性条件下的非相干电流算子,这是一种对于非均匀状态下电流分布的重要理论工具。作者通过分析,扩展了之前在空间平移不变情况下得出的热电导率表达式,提供了关于小频率行为的定量描述,这对于理解材料在不同能频范围内的性质至关重要。 文章进一步聚焦于全息理论框架,这是理论物理中用于模拟强相互作用和量子重力现象的强大工具。在这里,作者利用全息构建方法,展示了如何通过结合黑洞地平线上辅助流体的斯托克斯流解(一种描述粘性流动的数学模型)和与平衡黑洞解相关的特定热力学量,计算出非相干电流的直流电导率。这个结果不仅深化了我们对非平衡态下的输运性质的理解,而且可能对设计新型材料或优化电子设备的热管理有实际应用价值。 这篇论文不仅提供了一种新的理论视角来理解自发打破平移对称性的物质相的电流和热导特性,而且通过全息方法展示了理论物理在解决复杂系统中的实用性。它为凝聚态物理、量子场论和高能物理领域内的相关研究开辟了新的探索方向。
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JHEP04(2018)053
incoherent current and argue that when there is no superfluid the low frequency behaviour
of the thermoelectric conductivities can still be expressed in terms of certain thermody-
namics quantities as well as the finite incoherent DC conductivity, [σ
inc
]
DC
. Within a
holographic context, describing a strongly coupled system, we also explai n how [σ
inc
]
DC
can be calculated in terms of a Stokes flow on the spatially modulated black hole horizon,
supplemented with some thermodynamic quantities of the background. This extends the
results of [
4] that obtained the DC conduct i v i t i es for holographic systems for which the
translations are explicitly broken.
Naturally, we will focus on the properties of spatially modulated phases that are ther-
modynamically preferred. Such phases, which may have anisot r opi c spatial modulation,
necessarily satisfy the condition h
¯
T
ij
i = pδ
ij
, where
¯
T
ij
is the constant zero mode part
of the spatial components of the stress tensor [
5, 6]. However, since spatially modulated
phases in which this condition is not sat i sfi ed have been analysed in a holographic context
in [
7] we briefly comment on some of the modifie d formula in appendix A. In particular
our gener al results on how to derive the [σ
inc
]
DC
within holography immediately lead to
the result pres ented in [
7] for the specific holographic model s tud i ed there.
More generally, charge and spin density waves and their impact on the phenomenology
of condensed matter systems have been of central interest for a long time e.g. [
8]. Some more
recent work on thermoelectric transport for phases that spontaneously break translations
has appeared i n [
9], which included the effects of disorder and pinn i ng in a hydrody nami c
description, as well as in a number of holographic studies, incl ud i ng [
10–12] and brane
probe mo d el s [
13, 14]. An interesti ng open topic, which is left for the future, would be
to derive the effective hydrodynamic description of the specific exampl e s of spontaneously
formed density wave states which have already been studied within holography, along the
lines of [
15].
2 Boost invariant incoherent current
Consider a relativi s ti c quantum field theory at finite temperature defined on flat spacetime.
We will consider the system to be held at constant chemical potential, µ, with respect to an
abelian global symmetry. We will also allow for the possibility for additional deformations
of the Hamiltonian by a scalar operator O
φ
that is parametrised by the constant sou rc e φ
s
.
If O
φ
is odd under time reversal invariance then a non-zero φ
s
will explicitly break ti m e
reversal invariance.
We are particularly interested in phases in which spatial translations are broken spon-
taneously, but our analysis will also cover translationally invariant phases. We will assume
that the system reaches local thermodynamic equilibrium satisfying periodic boundary
conditions generated by a set of lattice vectors {L
i
}. Thus, the expectation values of the
stress tensor density, hT
µν
i, the conserved abelian current density, hJ
µ
i, as well hO
φ
i are
all functions of the spati al coordinate s, x, which are taken to be cartesian coordinates, that
are invariant unde r shifts by any of the lattice vectors. For any such function, A(x), the
zero mode is denoted by
¯
A, with
¯
A =
H
A ≡
1
vol
R
{L
i
}
{0}
dxA(x), whe r e the volume of a unit
cell of the lattice is vol ≡
R
{L
i
}
{0}
dx.
– 2 –
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