一维可精确求解流体中的无序基态
Disordered ground states in one-dimensional exactly solvable fluids
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中文总结 AI 辅助
研究一维可精确求解硬核流体，发现软排斥势为凹时在特定压强下存在无序基态，并给出其状态方程与关联函数，且这些基态非超均匀。
中文摘要 AI 辅助
在等温等压系综中，研究了直径为 $a$ 的经典硬核粒子的一维流体，粒子间通过有限程软排斥（单调递减）势 $\u03c6(x)=\u03b5 \left[ (a'-x)/(a'-a)\right]^{1/\u03bd}$（$a\le x\le a'$）成对相互作用，其中 $\u03b5$ 和 $\u03bd$ 为实正参数。若 $a'\le 2a$，则成对相互作用简化为最近邻相互作用，从而允许热平衡的精确解。我们关注 $T\to 0$ 的基态，特别是最近邻平均距离 $l_0$ 的状态方程和配对关联函数 $g_0(x)$。若 $\u03c6(x)$ 是凹的（$\u03bd\ge 1$），则存在一个“不可压缩性”压强 $p_i=\u03b5/(a'-a)$，使得当 $0<p<p_i$ 时基态为间距 $l_0=a'$ 的等距粒子链，当 $p>p_i$ 时基态为间距 $l_0=a$ 的等距粒子链。若 $\u03bd>1$（严格凹），则 $p=p_i$ 处的基态是无序的，$l_0=\left[ \nu a +(\nu-1)a'\right]/(2\nu-1)$，且 $g_0(x)$ 是离散位置上的加权 Dirac delta 函数的叠加。若 $\u03bd=1$（线性斜坡），则 $p=p_i$ 处的基态是无序的，$l_0=(a+a')/2$，且连续的 $g_0(x)$ 是 Heaviside 阶跃函数乘以 $x$ 的多项式的叠加。对于凹的 $\u03c6(x)$（$\u03bd\ge 1$），在 $p=p_i$ 处 $T=0$ 的等温磁化率非零，因此相应的无序基态是非超均匀的，即它们类似于非零温度下的无序流体。结果表明，仅出现在单一压强 $p_i$ 处的无序基态的配对关联函数，将其预测能力扩展到 $p_i$ 周围更宽压强范围内的非零温度热力学状态。
英文摘要
One-dimensional fluids of classical hard-core particles of diameter $a$, interacting in pairs via a soft repulsive (monotonically decreasing) potential of finite range $φ(x)=\varepsilon \left[ (a'-x)/(a'-a)\right]^{1/ν}$ $(a\le x\le a')$ with real positive parameters $\varepsilon$ and $ν$, are studied in an isothermal-isobaric ensemble. If $a'\le 2a$, the pairwise interactions are reduced to nearest-neighbour interactions, which allows for an exact solution of the thermal equilibrium. We focus on the $T\to 0$ ground states, specifically on the equation of state for the mean distance between nearest neighbours $l_0$ and the pair correlation function $g_0(x)$. If $φ(x)$ is concave $(ν\ge 1)$, there exists an ``incompressibility'' pressure $p_i=\varepsilon/(a'-a)$ such that the ground state is an equidistant chain of particles with spacing $l_0=a'$ for $0<p<p_i$ and with spacing $l_0=a$ for $p>p_i$. If $ν>1$ (strict concavity), the ground state at $p=p_i$ is disordered with $l_0=\left[ νa +(ν-1)a'\right]/(2ν-1)$ and $g_0(x)$ being a superposition of weighted Dirac delta functions over discrete positions. If $ν=1$ (linear ramp), the ground state at $p=p_i$ is disordered with $l_0=(a+a')/2$ and the continuous $g_0(x)$ is a superposition of Heaviside step functions multiplied by polynomials in $x$. The isothermal susceptibility at $T=0$ is nonzero for concave $φ(x)$ ($ν\ge 1$) at $p=p_i$ and, therefore, the corresponding disordered ground states are non-hyperuniform, i.e., they resemble disordered fluids at nonzero temperatures. It turns out that pair correlation functions of disordered ground states, which occur only at a single pressure $p_i$, extend their predictive power to thermodynamic states at nonzero temperatures over a wider range of pressures around $p_i$.
发表机构
- Institute of Physics, Slovak Academy of Sciences（斯洛伐克科学院物理研究所）
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