Numerical sign problem

<p>In <a href="/facts/Applied_mathematics/qyqklXXm">applied mathematics</a>, the numerical sign problem is the problem of numerically evaluating the <a href="/facts/Integral/V7lyV997">integral</a> of a highly <a href="/facts/Oscillation/6vSrm84a">oscillatory</a> <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> of a large number of variables. <a href="/facts/Numerical_methods/QT9cYa9z">Numerical methods</a> fail because of the near-cancellation of the positive and negative contributions to the integral. Each has to be integrated to very high <a href="/facts/Accuracy_and_precision/JQ47xXDq">precision</a> in order for their difference to be obtained with useful <a href="/facts/Accuracy_and_precision/JQ47xXDq">accuracy</a>.
</p><p>The sign problem is one of the major unsolved problems in the physics of <a href="/facts/Many-particle_system/n2rIxgwv">many-particle systems</a>. It often arises in calculations of the properties of a <a href="/facts/Quantum_mechanical/BRc3Mzgr">quantum mechanical</a> system with large number of strongly interacting <a href="/facts/Fermion/LEckdDsR">fermions</a>, or in field theories involving a non-zero density of strongly interacting fermions.
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Numerical sign problem open-in-new

Numerical sign problem