A New Phase Space Density for Quantum Expectations

8 years 19 days ago

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We introduce a new density for the representation of quantum states on phase space. It is constructed as a weighted diﬀerence of two smooth probability densities using the Husimi function and ﬁrst-order Hermite spectrograms. In contrast to the Wigner function, it is accessible by sampling strategies for positive densities. In the semiclassical regime, the new density allows to approximate expectation values to second order with respect to the high frequency parameter and is thus more accurate than the uncorrected Husimi function. As an application, we combine the new phase space density with Egorov’s theorem for the numerical simulation of time-evolved quantum expectations by an ensemble of classical trajectories. We present supporting numerical experiments in diﬀerent settings and dimensions. Key words. Time-dependent Schr¨odinger equation, Egorov’s theorem, expectation values, Husimi functions AMS subject classiﬁcations. 81S30,81Q20,65D30,65Z05

Johannes Keller, Caroline Lasser, Tomoki Ohsawa

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