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The kinetic energy term of Hamiltonian systems with balanced loss and gain isnot semi-positive-definite, leading to instabilities at the classical as wellquantum level. It is shown that an additional Lorentz interaction in theHamiltonian allows the kinetic energy term to be semi-positive-definite andthereby, improving the stability properties of the system. Further, aconsistent quantum theory admitting bound states may be obtained on the realline instead of Stoke wedges on the complex plane. The Landau Hamiltonian inpresence of balanced loss and gain is considered for elucidating the generalresult. The kinetic energy term is semi-positive-definite provided themagnitude of the applied external magnetic field is greater than the magnitudeof the `analogous magnetic field' due to the loss gain terms. It is shown thatthe classical particle moves on an elliptical orbit with a cyclotron frequencythat is less than its value in absence of the loss-gain terms. The quantumsystem share the properties of the standard Landau Hamiltonian, but, with themodified cyclotron frequency. It is shown that the Hall current hasnon-vanishing components along the direction of the external uniform electricfield and to its transverse direction. The Pauli equation in presence ofbalanced loss and gain is shown to be supersymmetric.

Taming Hamiltonian systems with balanced loss and gain via Lorentz interaction : General results and a case study with Landau Hamiltonian