Self-diffusion anomalies of an odd tracer in soft-core media

Abstract Odd-diffusive systems, characterised by broken time-reversal and/or parity, have recently been shown to display counterintuitive features such as interaction-enhanced dynamics in the dilute limit. Here we extend the investigation to the high-density limit of an odd tracer embedded in a soft medium described by the Gaussian core model (GCM) using a field-theoretic approach based on the Dean–Kawasaki equation. Our analysis reveals that interactions can enhance the dynamics of an odd tracer even in dense systems. We demonstrate that oddness results in a complete reversal of the well-known self-diffusion ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) anomaly of the GCM. Ordinarily, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> exhibits a non-monotonic trend with increasing density, approaching but remaining below the interaction-free diffusion, D 0 , ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> ) so that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">↑</mml:mo> <mml:msub> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> at high densities. In contrast, for an odd tracer, self-diffusion is enhanced ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:msub> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> ) and the GCM anomaly is inverted, displaying <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">↓</mml:mo> <mml:msub> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> at high densities. The transition between the standard and reversed GCM anomaly is governed by the tracer’s oddness, with a critical oddness value at which the tracer diffuses as a free particle ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>D</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≈</mml:mo> <mml:msub> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> ) across all densities. We validate our theoretical predictions with Brownian dynamics simulations, finding strong agreement between the them.