{'fraction_non_alphanumeric': 0.03482045701849837, 'fraction_numerical': 0.006528835690968444, 'mean_word_length': 4.508982035928144, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A path integral approach to electronic friction of a nanometer-sized tip scanning a metal surface

In this work, we study the dissipation mechanism and frictional force of a nanometer-sized tip scanning a metal surface via a path integral approach. The metal, with internal degrees of freedom (c, c †) and a tip with an internal degree of freedom (d, d †) couple with one another by means of an exchanged potential, V. Having integrated out all internal degrees of freedom, we obtain the in-out amplitude. Moreover, we calculate the imaginary part of the in-out amplitude and the frictional force. We find the imaginary part of the in-out amplitude to be positive, and correlated to the sliding velocity in most cases. The frictional force is proportional to the sliding velocity for the case where v < 0.01. However, for cases where v > 0.01, the frictional force demonstrates nonlinear dependence on sliding velocity.